FIN3403 Chapter 5
You are looking at an investment that will pay $1,200 in 5 years if you invest $1,000 today. What is the implied rate of interest?
r = (1,200 / 1,000)1/5 - 1 r = (FV/PV)^1/t - 1
Find N (t)
t = ln(FV / PV)/ ln(1+r)
Total Interest
Simple + Compound Interest
FVIF (Future Value Interest Factor)
(1+r)^t
Suppose you are offered an investment that will allow you to double your money in 6 years. You have $10,000 to invest. What is the implied rate of interest?
(20000/10000)^1/6 -- 1 =12.25%
Investment pays 12 percent per year. You invest $400. How much will you have in 3 years? How much will you have in 7 years? How much interest did you earn over the 7 years? How much of the interest is from compounding?
1. $400 (1.12)^3 = 561.97 2. $400 (1.12)^7 = 884.27 3. 884.27 - 400 = 484.27 4. Simple interest = 400 x .12 = $48/yr x 7 = $336
PVIF (Present Value Interest Factor)
1/(1+r)^t
Suppose you need to have $10,000 in 10 years and you can earn 6.5% on your money. How much do you need to invest today to reach your goal?
10000/(1+.065)^10 = 5327.26
Suppose you need $10,000 in one year for the down payment on a new car. If you can earn 7% annually, how much do you need to invest today?
10000/(1+.07)^1 = 9345.79
Present Value
Current value of future cash flows discounted at the appropriate discount rate
You want to begin saving for your daughter's college education and you estimate that she will need $150,000 in 17 years. If you feel confident that you can earn 8% per year, how much do you need to invest today?
150000/(1.08)^17 = 40,540.34
Suppose you had a relative deposit $10 at 5.5% interest 200 years ago. How much would the investment be worth today? What is the effect of compounding?
= 447,189.84 Simple Interest would be = $10 + $10(.055) x 200 yrs = $120
Present Value, Time Period & Interest Rate Relationship
For a given interest rate - the longer the time period, the lower the present value
Present Value, Time Period & Interest Rate Relationship
For a given time period - the higher the interest rate, the smaller the present value
Compound Interest
Interest you earn off interest Compounding effects is greatest a longer horizons
Suppose you invest $1,000 for one year at 5% per year. What is the future value in one year? Suppose you leave the money in for another year. How much will you have two years from now?
N = 1 I/Y = 5 PV = 1000 PMT = 0 FV = ? ===1050 calculator or ===(1000)(1.05)^1 N = 2 I/Y = 5 PV = 1000 PMT = 0 FV = ? ===1102.5
Simple Interest
The interest that you earn on the money you contributed