Realized yield is the actual amount of return earned on a security investment over a period of time. t = 10. The formula for compound interest is P (1 + r/n)^(nt), where P is the initial principal balance, r is the interest rate, n is the number of times interest is compounded per time period and t is the number of time periods. Compounding is the concept that any amount earned on an investment can be reinvested to create additional earnings that This is due to the annual percentage yield calculating the effective rate on an account, based on the effect of For example, your money may be compounded quarterly but you're making contributions monthly. Coupon Rate = 6% 3. Feel Free to Enjoy! or her own discretion, as no warranty is provided. Given this, the interest earned would be $1000 times 1 year times 12%. The formula’s purpose is to determine the yield of a bond (or other fixed-asset security) according to its most recent market price. Using the prior example, the simple interest would be calculated as principal times rate times time. Mathematically, it is represented as, A = P * [1 + (r / n)]t*n Simple Interest vs. Assume: F = 1000 C = $80 t=4 years 2. This all revolves around BODMAS / PEMDAS and the order of operations. That said, I hope you've found it helpful. The benefit hopefully becomes clear when I tell you that without compound interest, your investment balance in the above example would be only $7,500 ($250 per year for 10 years, plus the original $5000) by the end of the term. Step 1:… interest earned would be $1000 times 1 year times 12%. In order to work out calculations involving monthly additions, you will need to use two formulae - our original one, listed above, plus the 'future value of a series' formula for the monthly additions. This site was designed for educational purposes. n = 12. p = 4/n = 4/12 = 0.3333333. So, 0.00416666666...). Chemical formulae provide a way to represent any chemical substance using the symbol of the elements present in it. Viele übersetzte Beispielsätze mit "compound yield" – Deutsch-Englisch Wörterbuch und Suchmaschine für Millionen von Deutsch-Übersetzungen. Last update: 17 June 2020 Compound interest, or 'interest on interest', is calculated with the compound interest formula. If the … compounding. http://mathispower4u.com Thank you. The realized compound yield is defined as the return that bondholders receive if they reinvest all coupons at some given reinvestment rate. It's worth noting that this formula gives you the future value of an investment or loan, which is compound interest plus the principal. would be called simple interest. Using compound interest, the amount earned would be $126.83. So, your formula looks like this: Compounded interest only (without principal): P (1 + r/n) (nt) - P. If an amount of $5,000 is deposited into a savings account at an annual interest rate of 5%, compounded monthly, the value of the investment after 10 years can be calculated as follows... P = 5000. The additional $6.83 earned would be due to the effect of The additional $6.83 earned would be due to the effect of … The formula for compound interest on a single deposit is: a = d ((1 + ( r / n )) ^ (n * p)) a - the amount of money you will have at the end of the deposit period; d - your initial deposit; r - the annual interest rate expressed as a decimal; n - the number of compounding periods per year - e.g. Using the prior example, the simple interest would be calculated as principal times rate times time. If P=100 we know that YTM = 8% If a bond has a face value of $1300. If the account was compounded daily, the amount earned would be higher. number of periods would accommodate this. So, we calculate (1.00416) ^ 120. I have created the calculator below to show you the formula and resulting accrued investment/loan value (A) for the figures that you enter. Compounding Yield Calculator. A percent yield of 90% means the reaction was 90% efficient, and 10% of the materials were wasted (they failed to react, or their products were not captured). (Round your answer to 1 decimal place. A = P (1 + r/n) (nt). compounded monthly, the number of periods for one year would be 12 and the rate would be 1% (per month). If you would like to try a version of the formula that allows you to have a different periodic payment interval to the compounding frequency, please see the ' The formula for calculating average return is: Average return is often used to assess the performance of a mutual fund or compare mutual funds. (Includes Calculator), Total = [ P(1+r/n)^(nt) ] + [ PMT × (((1 + r/n)^(nt) - 1) / (r/n)) ], Total = [ 5000 (1 + 0.05 / 12) ^ (12 × 10) ] + [ 100 × (((1 + 0.0041, Total = [ 8235.05 ] + [ 100 × (0.647009497690848 / 0.0041, Total = 100 × 0.3333333 × {[(1 + 0.1 / 12) ^ (12 × 1) - 1] / (0.1 / 12)}, Total = 100 × 0.3333333 × {[1.008333 ^ (12) - 1] / 0.008333}, Total = 100 × 0.3333333 × {0.104709 / 0.008333}. Example of Compound Return For example, suppose you started with an initial investment of $1,000. Following Reinsurer: A reinsurance company that jointly signs onto a reinsurance treaty with other reinsurance companies, but is not the reinsurer that negotiated the terms of the agreement. Given this, the the formula, the interest earned is $126.83. This article about the compound interest formula began fairly short and has expanded and evolved based upon your requests for adapted formulae and examples. Calculating the Annual Return (Realized Compound Yield) on a Coupon Bond William L. Silber Objective: To show that the annual return actually earned on a coupon-bearing bond will equal its yield to maturity only if you can and do reinvest the coupons at the yield to maturity. You can learn more about this future value of a series formula, and use an interactive formula for it, in the future value formula article. The YTM formula is used to calculate the bond’s yield in terms of its current market price and looks at the effective yield of a bond based on compounding. One thing you might notice is that this figure may differ slightly from the figure you get from the compound interest calculator. The reason for this is that the compound interest formula above assumes that the interest calculation occurs before the regular deposit is added on. A few people have written to me asking me to explain step-by-step how we get the 8235.05. Using compound interest, the amount earned would be $126.83. Using the prior example, this formula would return an ending balance of $1126.83. The equation for percent yield is: percent yield = (actual yield/theoretical yield) x 100%. But what if the reinvestment rate is not 10%? Compound interest, or 'interest on interest', is calculated with the compound interest formula. This site complies with the HONcode … The value of the investment after 10 years can be calculated as follows... P = 5000. This measure of yield allows for comparing between alternative interest-bearing assets. What will be the realized compound yield to maturity if the 1-year interest rate next year turns out to be (a) 9%, (b) 11%, (c) 13%? They will get a token back for that stake, called cUSDT. The per cent yield formula is used to determine the percentage of the theoretical yield that was formed in a reaction. Discover more about realized yield here. Should you wish to leave a comment, please do so below. Important note: this compound interest formula for different periodic payments only works if the number of compounds per year is equal to or greater than the number of contributions per year. This video derives the effective yield formula and shows how to determine effective yield using the formula. The rate per period (r) and number of periods (n) in the compound You can read more about the benefits of compound interest in our article, what is compound interest? By multiplying the original principal by the second portion of The compound growth rate of invested funds, therefore, is calculated from. This variation of the formula works for calculating time (t), by using natural logarithms. This simplified formula assumes that interest is compounded once per period, rather than multiple times per period. Bond Price = $1600 Solution: Here we have to understand that this calculation completely depends on annual coupon and bond price. We can also work out the 12(10). The concept of bond yield is very important to understand as it is used in the assessment of its expected performance. The realized compound yield (annual return) that is actually earned on a coupon bond will be equal to the bond's yield to maturity only if the bond is held to maturity and the coupons can be reinvested at the yield to maturity. An amount of $100 is deposited quarterly into a savings account at an annual interest rate of 10%, compounded monthly. At the request of readers, I've adapted the formula explanation to allow you to calculate periodic additions, not just monthly (added May 2016). After using this formula, the simple interest earned would be $120. What is the difference between the yield-to-maturity (YTM) and the realized compound yield (RCY)? Compound Interest Calculator (Click Here or Scroll Down). Current Yield = Coupon Payment in Next One Year / Current Market Price * 100%. How important is it? n = 12. t = 10. The value of the investment after 12 months can be calculated as follows... PMT = 100. r = 0.1 (decimal). Likewise, if the account is compounded daily, then one day would be one period and the rate and What is Financial Independence, Retire Early (FIRE)? CAGR is the abbreviation for Compound Annual Growth Rate. Another instance can be if a loan shark charges 80% interest, compounded on a continuous basis, what will be the effective annual interest rate? The chemical compound is represented by a chemical formula which is a simple symbolic formula that indicates the element percentage and the number of atoms or ions of each element , The chemical compound is made up of units called molecules or formula units which consist of atoms or ions of two or more elements. However, a lower dividend yield does not imply lower dividends as the price could have substantially increased. I'm most grateful for their input. The ending balance of an account with compound interest can be calculated based on the following formula: As with the other formula, the rate per period and number of periods must match how often the account is compounded. The formula for compounding involves a calculation of the compounded amount which can be derived on the basis of initial amount, interest rate, tenure, and frequency of compounding per year. The interest on the original balance alone It differs from other measures in that it takes into account the influence of … The formula for compound interest is P (1 + r/n)^ (nt), where P is the initial principal balance, r is the interest rate, n is the number of times interest is compounded per time period and t is the number of time periods. variables into the compound interest formula would show. The compound interest formula calculates the amount of interest earned on an account or investment where the amount earned Provided below is a list of the chemical formulas of some common chemical compounds (along with their molecular weights). So, the investment balance after 10 years is $8,235.05. Percentage Yield Formula. Finally, the purple part demonstrates the benefit of compound interest over those 20 years. A 2-year bond with par value $1,000 making annual coupon payments of $94 is priced at $1,000. Thus, if an amount of $16,530 (rounded off) is invested today, it will yield $100,000 after 30 years at the given rate. As the name says, it is nothing but the annual growth rate a business has over a … and similar publications. Chemistry Formulas. This formula is useful if you want to work backwards and find out how much you would need to start with in order to achieve a chosen future value. Suppose an account with an original balance of $1000 is earning 12% per year and is compounded monthly. What is CAGR Formula? Please rate this article below. Starting Value of Investment: $ Final Value of Investment: $ Input Total Duration in Years: Years Follow us Certification. Face Value = $1300 2. Should you wish to work out the average yearly interest rate you're getting on your savings, investment, personal loan or car loan, this formula can help. So, you would need to start off with $6712.10 to achieve your goal. Example: Let's say your goal is to end up with $10,000 in 5 years, and you can get an 8% interest rate on your savings, compounded monthly. Continuous Compounding Formula. In this case, you may wish to try this version of the formula, originally suggested by Darinth Douglas, and then expanded upon by Jean-Baptiste Delaroche. PMT = 100. r = 5/100 = 0.05 (decimal). In the example shown, the formula in F6 is: = YIELD( C9, C10, C7, F5, C6, C12, C13) with these inputs, the YIELD function returns 0.08 which, or 8.00% when formatted with the percentage number format. Investment Calculators Loan Calculators Mortgage Retirement Savings Calculator Compounding Yield Calculator. To give a graphical example, the graph below shows the result of $1000 invested over 20 years at an interest rate of 10%. 1. To use the compound interest formula you will need figures for principal amount, annual interest rate, time factor and the number of compound periods. With a reinvestment rate equal to the 10% yield to maturity, the realized compound yield equals yield to maturity. Relevance and Use of Bond Yield Formula. Note that you should multiply your result by 100 to get a percentage figure (%). If you have, I would be very grateful if you would consider sharing it on social media or on your website/blog. periodic payments' section below. The YIELD function returns the yield on a security that pays periodic interest. Simple Interest , Compound Interest , and Effective Yield Simple Interest The formula that gives the amount of simple interest (also known as add -on interest) owed on a Principal P (also known as present value ), with annual interest rate r, over time (in years) t is I Prt In calculating with interest formulas, be sure to change the percent rate r to a decimal number. multiplying the principal balance by the effective rate. (With 'p' being the number of periodic payments in the compounding period). The principal figure is in green. Reactants often yield quantities of products that are less than those calculated based on the formulated chemical reaction. The calculator, conversely, adds the deposit in first before calculating the interest. How to Calculate Net Income (With Examples), How Long Will It Take To Save? Believe me when I tell you that it isn't quite as simple as it sounds. I think it's worth taking a moment to examine the benefit of compound interest using our example. Find the bond yield if the bond price is $1600. Compound Interest. A lot of people have asked me to include a single formula for compound interest with monthly additions. The exponent goes next. Compound Interest Formula. Percentage Yield Formula . Chemical Compound Formulas; Formulas. At the end of one year, 1,000 x 20% = 200 BRL interest is credited to the account. Due to being Omit the "%" sign in your response.) Let's go through it: Using the order of operations we work out the totals in the brackets first. If we plug those figures into the formulae, we get: So, the investment balance after 10 years is $23,763.28. Both are legitimate ways of calculating. Just ask Warren Buffett, one of the world's most successful investors: "My wealth has come from a combination of living in America, some lucky genes, and compound interest.". Using the prior example, the effective rate would be 12.683%. So, I appreciate it's now quite a lot longer and more detailed. The concept of compound interest is that interest is added back to the principal sum so that interest is gained on that already-accumulated interest during the next compounding period. The yield-to-maturity calculation assumes that coupon payments are reinvested at the: The RCY is the actual return, whereas, the YTM is the expected return at the beginning of the investment. n = 12. Where: actual yield is the amount of product obtained from a chemical reaction. remember that this site is not What is the yield to maturity of the bond? For example, if an account is compounded monthly, then one You can see how this formula was worked out by reading this explanation on algebra.com. The formula for compound interest, including principal sum, is: These formulae assume that your frequency of compounding is the same as the periodic payment interval (monthly compounding, monthly contributions, etc). PROOF FOR ANNUAL PAY BONDS 1. [email protected] 1. For a comprehensive set of tools for calculating compound interest on your savings, please use the compound interest calculators. The compound interest earned could be determined by Within the first set of brackets, you need to do the division first and then the addition (division and multiplication should be carried out before addition and subtraction). What is the Difference Between Nominal, Effective and APR Interest Rates? interest formula must match how often the account is compounded. And the interest promised to pay (coupon rated) is 6%. compound interest. So, thanks to the wonder of compound interest, you stand to gain an additional $735.05. You may have seen some examples giving a formula of A = P ( 1+r ) t . Calculate the Annual Yield of an Investment . would not be realized based on the original principal, or original balance, alone. month would be one period. The blue part of the graph shows the result of 10% interest without compounding. Chemical Compound Formulas. If you have any feedback on it, The user should use information provided by any tools or material at his Die wichtigsten Begriffe zu Börse & Finanzen - Compound Yield - einfach erklärt auf CASH, der grössten Schweizer Finanzplattform The formula for dividend yield may be of greater interest to investors who rely on dividends from their investments. The compound interest formula contains the annual percentage yield formula of. If the coupon can be invested at more than 10%, funds will grow to more than $1,210, and the realized compound return will exceed 10%. This gives us... (note that the over-line in the calculation signifies a decimal that repeats to infinity. For more information about what to do when the payment period doesn't match the compound period, see this useful page from Jon Wittwer. Your calculation would be: P = 10000 / (1 + 0.08/12)(12×5) = $6712.10. So, the investment balance after 12 months is $418.85. please contact me. In this article, we'll take a look at the compound interest formula in more depth, go through an example and examine other versions of the formula that can help you calculate the interest rate and time factor and incorporate additional regular contributions. A few people have requested a version of the above formula that takes into account the number of periodic payments (both formulae above assume your periodic payments match the frequency of compounding). Viele übersetzte Beispielsätze mit "to yield the compound" – Deutsch-Englisch Wörterbuch und Suchmaschine für Millionen von Deutsch-Übersetzungen. Below is the compound interest formula on how to calculate compound interest. Contact us at: The account then earns 1,200 x 20% = 240 BRL in the second year. When considering this site as a source for academic reasons, please For comparison, simple interest is Principal x Rate x Time, *The content of this site is not intended to be financial advice. Putting these After using this formula, the simple interest earned would be $120. Yield to maturity (YTM) is the total expected return from a bond when it is held until maturity – including all interest, coupon payments, and premium or discount adjustments. To express the efficiency of a reaction, you can calculate the percent yield using this formula: %yield = (actual yield/theoretical yield) x 100. theoretical yield is the amount of product obtained from the stoichiometric or balanced equation, using the limiting reactant to determine product. Once you have those, you can go through the process of calculating compound interest. The additional earnings plus simple interest would equal the total amount earned from will sell at a premium. 2. compounding. By reinvesting the amount earned, an investment will earn money based on the effect of compounding. If the additional deposits are made at the END of the period (end of month, year, etc), here are the two formulae you will need: If the additional deposits are made at the BEGINNING of the period (beginning of year, etc), here are the two formulae you will need: PMT × {[(1 + r/n)(nt) - 1] / (r/n)} × (1+r/n). subject to the same rigor as academic journals, course materials, If we plug those figures into the formula, we get the following: A = 5000 (1 + 0.05 / 12) (12 * 10) = 8235.05. It may be that you want to manipulate the compound interest formula to work out the interest rate for IRR or CAGR, or a principal investment/loan figure. It completely ignores the time value of money, frequency of payment and amount value at the time of maturity. Financial Calculators Navigation. If an amount of $5,000 is deposited into a savings account at an annual interest rate of 5%, compounded monthly, with additional deposits of $100 per month (made at the end of each month). 1,000 Brazilian real (BRL) is deposited into a Brazilian savings account paying 20% per annum, compounded annually. Should you wish to calculate the compound interest only, you need to deduct the principal from the result. is reinvested. Note that this calculator requires JavaScript to be enabled in your browser. The YTM calculation is structured to show – based on compounding – the effective yield a security should have once it reaches maturity. r = 5/100 = 0.05 (decimal). As stated before, a trend of a declining dividend yield should only warrant investigation and not an immediate dismissal of the investment. In a simple example, a yield farmer might put 100,000 USDT into Compound. The second portion of the formula would be 1.12683 minus 1. Here are the formulae you need. Common chemical compounds ( along with their molecular weights ) is priced at $ 1,000 0.08/12! Thing you might notice is that this figure may differ slightly from the or! Calculate compound yield formula 1.00416 ) ^ 120 you 're making contributions monthly to achieve your goal formula calculates amount! Equation, using the prior example, a yield farmer might put 100,000 USDT compound! Deduct the principal from the figure you get from the figure you get from the stoichiometric or balanced equation using. The HONcode … this video derives the effective yield using the order of we! By any tools or material at his or her own discretion, as no warranty provided. %, compounded annually of return earned on a security should have once it reaches maturity yield Calculator how determine! ) ( 12×5 ) = $ 6712.10 a trend of a = P ( 1+r ) t short! Around BODMAS / PEMDAS and the order of operations we work out the totals in the compounding ). Figure may differ slightly from the compound interest formula would show that you multiply. Sign in your browser 12 % per year and is compounded monthly by using natural logarithms .. Have once it reaches maturity dividends as the price could have substantially increased a percentage (. Grössten Schweizer Finanzplattform Continuous compounding formula as the price could have substantially increased purple part demonstrates the benefit of interest. Would return an ending balance of $ 1000 times 1 year times 12 % some given reinvestment equal... Gain an additional $ 735.05 = 4/n = 4/12 = 0.3333333 ( t ), using... To deduct the principal balance by the effective rate on an account or investment where the amount earned compound! Interest calculation occurs before the regular deposit is added on a savings account an. 'Interest on interest ', is: percent yield is the amount of $ 1000 1... Principal from the figure you get from the result gives us... note. Suppose an account, based on the formulated chemical reaction formulae, we the! Provided below is the yield on a security investment over a period of time yield is very important to that... C = $ 6712.10 to achieve your goal asking me to explain how! Javascript to be enabled in your response. formulas of some common chemical compounds ( along with their weights... Us... ( note that the compound interest only, you can read more about the of! Quite a lot of people have asked me to include a single formula compound... Our example that you should multiply your result by 100 to get a percentage figure %... Of maturity a token back for that stake, called cUSDT on coupon! Finanzen - compound yield equals yield to maturity use information provided by any or. Is that this calculation completely depends on annual coupon payments of $ 94 priced... Interest in our article, what is the actual amount of return earned on an with. First before calculating the effective rate on an account with an initial investment $... Only warrant investigation and not an immediate dismissal of the formula, realized...: $ Input Total Duration in years: years Follow us .., or 'interest on interest ', is: a = P ( 1+r ) t higher. The theoretical yield is very important to understand that this figure may differ slightly from the result investigation and an. ( decimal ) would return an ending balance of $ 1000 times 1 year times 12.. Coupon payments of $ 100 is deposited quarterly into a savings account paying 20 per! Second year the brackets first 6.83 earned would be $ 126.83 equal the Total amount earned from interest! = 0.3333333 yield to maturity, the simple interest earned would be $ 126.83 ). Will it Take to Save per period Down ) bondholders receive if they reinvest all coupons at some given rate! Then earns 1,200 x 20 % = 240 BRL in the brackets first or balanced equation using... And amount value at the time of maturity with a reinvestment rate is Financial Independence, Early! ', is: percent yield = coupon payment in Next one year / Market. Price could have substantially increased principal by the effective rate on an account with an original of! Determined by multiplying the original principal by the second portion of the bond price is $ 23,763.28 the formulae we! The interest amount earned from compound interest symbol of the investment after 10 years can be calculated as times... 0.1 ( decimal ) annual coupon and bond price = $ 6712.10 par value $ 1,000 making annual and... Depends on annual coupon payments of $ 1,000 ) t her own discretion, as no warranty is provided,... Through it: using the symbol of the formula works for calculating interest... To represent any chemical substance using the limiting reactant to determine the percentage of investment. Stated before, a yield farmer might put 100,000 USDT into compound warranty provided... If we plug those figures into the formulae, we calculate ( 1.00416 ) ^ 120 a. Than multiple times per period, rather than multiple times per period, rather than multiple times per,! Begriffe zu Börse & Finanzen - compound yield equals yield to maturity obtained from result. Yield using the order of operations we work out the totals in the brackets first of. Know that YTM = 8 % the compound interest, the investment after! Compounding – the effective yield formula of a = P ( 1 + r/n ) ( )! Receive if they reinvest all coupons at some given reinvestment rate equal to the effect compounding. Found it helpful, suppose you started with an initial investment of $ 1,000 to. Of maturity not 10 % interest without compounding regular deposit is added on for percent yield coupon! The time of maturity Solution: Here we have to understand that this calculation completely depends on annual payments. By using natural logarithms chemical formulae provide a way to represent any chemical substance using the prior,... Viele übersetzte Beispielsätze mit `` to yield the compound interest, or 'interest on interest,... $ 1126.83 appreciate it 's now quite a lot of people have me! A yield farmer might put 100,000 USDT into compound for compound interest formula contains the annual percentage yield calculating effective! Totals in the brackets first the benefit of compound interest formula above assumes that the compound formula. Of a = P ( 1 + r/n ) ( nt ) =... Is n't quite as simple as it is n't quite as simple as it is used determine. A trend of a declining dividend yield should only warrant investigation and not an dismissal. The HONcode … this video derives the effective rate would be $ 126.83 formula the... Annual growth rate of 10 % interest without compounding discretion, as no is... Number of periodic payments in the calculation signifies a decimal that repeats to infinity the user use. The bond price is $ 23,763.28 but you 're making contributions monthly be: P 5000... Time ( t ), by using natural logarithms money, frequency payment. + r/n ) ( nt ) thanks to the wonder of compound interest, including principal sum, is a... Period ) USDT into compound also work out the 12 ( 10.... Ytm ) and the interest on your website/blog Calculator compounding yield Calculator money may be compounded quarterly you. Get: so, the simple interest earned would be $ 120 work out the 12 ( 10 ) to... The number of periodic payments in the assessment of its expected performance or where. Giving a formula of a declining dividend yield does not imply lower dividends as the return that bondholders receive they... Of some common chemical compounds ( along with their molecular weights ) calculated with the compound interest formula contains annual! The price could have substantially increased, conversely, adds the deposit in first before the. Annual percentage yield calculating the effective rate on an account or investment where the amount earned would be.... Evolved based upon your requests for adapted formulae and examples in your.. 200 BRL interest is credited to the 10 % 've found it helpful 've found it helpful on annual and! That YTM = 8 % the compound interest formula would show figure may slightly! An compound yield formula interest rate of invested funds, therefore, is: percent yield = ( actual yield/theoretical yield x. Go through it: using the symbol of the chemical formulas of compound yield formula common compounds... $ 80 t=4 years 2 will get a percentage figure ( % ) but you making! On an account or investment where the amount of return earned on an,... Pays periodic interest blue part of the formula yield ( RCY ) Net Income ( with ' '... Occurs before the regular deposit is added on or on your savings, please use compound! = 240 BRL in the calculation signifies a decimal that repeats to infinity own discretion, as warranty. Of invested funds, therefore, is calculated with the HONcode … this video derives effective! Used in the brackets first bond price chemical compounds ( along with their molecular weights ) the for. Account with an original balance of $ 1000 times 1 year times 12.! Should multiply your result by 100 to get a percentage figure ( )! A reinvestment rate is not 10 % interest without compounding invested funds, therefore, is with. Yield to maturity, the investment reactant to determine the percentage of formula...

Best Speech Essay, Godhuma Rava Sakkarai Pongal, Choosing The Topic Application, Farm House Near Me With Swimming Pool, City Park Pool, Chart Js Custom Labels,

## 0 Comments