Question

You are hoping to buy a house in the future and recently received an inheritance of ​$20 000. You intend to use your inheritance as a down payment on your house. a.  If you put your inheritance in an account that earns 8 percent interest compounded​ annually, how many years will it be before your inheritance grows to ​$33 000​? b.  If you let your money grow for 10.25 years at 8 percent​, how much will you​ have? c.  How long will it take your money to grow to ​$33000 if you move it into an account that pays 5 percent compounded​ annually? How long will it take your money to grow to ​$33000 if you move it into an account that pays 11 percent​? d.  What does all this tell you about the relationship among interest​ rates, time, and future​ sums? a.  If you put your inheritance in an account that earns 8 percent interest compounded​ annually, how many years will it be before your inheritance grows to ​$33000​?

Answer 1

a. Time required

Future Value = Present Value * (1 + r)^n

33000 = 20000 * (1 + 0.08)^n

1.65 = 1.08^n

Apply Logarithm on both sides, we get

ln 1.65 = n * ln 1.08

0.217484 = n * 0.033424

n = Number of Years = 6.51 Years

b. Future Value = $20000 x (1.08)^10.25 = $20000 x 2.200865 = $44017.31

c1. 5% interest

Future Value = Present Value * (1 + r)^n

33000 = 20000 * (1 + 0.05)^n

1.65 = 1.05^n

Apply Logarithm on both sides, we get

ln 1.65 = n * ln 1.05

0.217484 = n * 0.021189

n = Number of Years = 10.26 Years

c2. 11% interest

Future Value = Present Value * (1 + r)^n

33000 = 20000 * (1 + 0.05)^n

1.65 = 1.11^n

Apply Logarithm on both sides, we get

ln 1.65 = n * ln 1.11

0.217484 = n * 0.045323

n = Number of Years = 4.80 Years

d. the conclusions are

when interest rates increase keeping time constant, the future sum will increase

when time increase keeping interest rate constant, the future sum will increase

Interest Rate and Time are directly proportional to Future Sum