Present value what and future value and suppose you

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Unformatted text preview: an solve for the fourth If you are using a financial calculator, be sure If and remember the sign convention or you will receive an error (or a nonsense answer) when solving for r or t solving 20 Discount Rate Often we will want to know what the implied Often interest rate is in an investment interest Rearrange the basic PV equation and solve for r FV = PV(1 + r)t r = (FV / PV)1/t – 1 If you are using formulas, you will want to make If use of both the yx and the 1/x keys use 21 Discount Rate – Example 1 You are looking at an investment that will pay You $1,200 in 5 years if you invest $1,000 today. What is the implied rate of interest? What r = (1,200 / 1,000)1/5 – 1 = .03714 = 3.714% Calculator – the sign convention matters!!! • • • • N=5 PV = -1,000 (you pay 1,000 today) FV = 1,200 (you receive 1,200 in 5 years) CPT I/Y = 3.714% 22 Discount Rate – Example 2 Suppose you are offered an investment Suppose that will allow you to double your money in 6 years. You have $10,000 to invest. What is the implied rate of interest? What r = (20,000 / 10,000)1/6 – 1 = .122462 = 12.25% 12.25% 23 Discount Rate – Example 3 Suppose you have a 1-year old son and Suppose you want to provide $75,000 in 17 years towards his college education. You currently have $5,000 to invest. What interest rate must you earn to have the $75,000 when you need it? $75,000 r = (75,000 / 5,000)1/17 – 1 = .172688 = 17.27% 17.27% 24 Quick Quiz – Part III What are some situations in which you might want to What know the implied interest rate? know You are offered the following investments: You can invest $500 today and receive $600 in 5 years. The You investment is considered low risk. investment You can invest the $500 in a bank account paying 4%. What is the implied interest rate for the first choice and which What investment should you choose? investment 25 Finding the Number of Periods Start with basic equation and solve for t Start (remember your logs) (remember FV = PV(1 + r)t t = ln(FV / PV) / ln(1 + r) You can use the financial keys on the You calculator as well; just remember the sign convention. convention. 26 Number of Periods – Example 1 You want to purchase a new car and you You are willing to pay $20,000. If you can invest at 10% per year and you currently have $15,000, how long will it be before you have enough money to pay cash for the car? the t = ln(20,000 / 15,000) / ln(1.1) = 3.02 years 27 Number of Periods – Example 2 Suppose you want to buy a new house. You Suppose currently have $15,000 and you figure you need to have a 10% down payment plus an additional 5% of the loan amount for closing costs. Assume the type of house you want will cost about $150,000 and you can earn 7.5% per year, how long will it be before you have enough money for the down payment and closing costs? closing 28 Number of Periods – Example 2 Number Continued Continued How much do you need to have in the future? Down payment = .1(150,000) = 15,000 Closing costs = .05...
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