Tvm formula that can be found in a another

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Unformatted text preview: Example Another Suppose you borrow $2,000 at 5% and you are Suppose going to make annual payments of $734.42. How long before you pay off the loan? How 2,000 = 734.42(1 – 1/1.05t) / .05 .136161869 = 1 – 1/1.05t 1/1.05t = .863838131 1.157624287 = 1.05t t = ln(1.157624287) / ln(1.05) = 3 years 29 Finding the Rate Suppose you borrow $10,000 from your Suppose parents to buy a car. You agree to pay $207.58 per month for 60 months. What is the monthly interest rate? monthly Sign convention matters!!! 60 N 10,000 PV -207.58 PMT CPT I/Y = .75% 30 Annuity – Finding the Rate Annuity Without a Financial Calculator Without Trial and Error Process Choose an interest rate and compute the PV of the Choose payments based on this rate payments Compare the computed PV with the actual loan amount If the computed PV > loan amount, then the interest rate If is too low is If the computed PV < loan amount, then the interest rate If is too high is Adjust the rate and repeat the process until the computed Adjust PV and the loan amount are equal PV 31 Quick Quiz – Part III You want to receive $5,000 per month for the next 5 You years. How much would you need to deposit today if you can earn .75% per month? you What monthly rate would you need to earn if you only What have $200,000 to deposit? have Suppose you have $200,000 to deposit and can earn . 75% per month. How many months could you receive the $5,000 How payment? payment? How much could you receive every month for 5 years? 32 Future Values for Annuities Suppose you begin saving for your Suppose retirement by depositing $2,000 per year in an IRA. If the interest rate is 7.5%, how much will you have in 40 years? much FV = 2,000(1.07540 – 1)/.075 = 454,513.04 33 Annuity Due You are saving for a new house and you You put $10,000 per year in an account paying 8%. The first payment is made today. How much will you have at the end of 3 years? years? FV = 10,000[(1.083 – 1) / .08](1.08) = 35,061.12 35,061.12 34 Annuity Due Timeline 0 10000 1 10000 2 3 10000 32,464 35,016.12 35 Perpetuity – Example 6.7 Perpetuity formula: PV = C / r Current required return: 40 = 1 / r r = .025 or 2.5% per quarter Dividend for new preferred: 100 = C / .025 C = 2.50 per quarter 36 Quick Quiz – Part IV You want to have $1 million to use for You retirement in 35 years. If you can earn 1% per month, how much do you need to deposit on a monthly basis if the first payment is made in one month? one What if the first payment is made today? You are considering preferred stock that pays a You quarterly dividend of $1.50. If your desired return is 3% per quarter, how much would you be willing to pay? be 37 Work the Web Example Another online financial calculator can be found Another at MoneyChimp at Click on the web surfer and work the following Click example example Choose calculator and then annuity Choose You just inherited $5 million. If you can earn 6% on You your money, how much can you withdraw each year for the next 40 yea...
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