Question

You are hoping to buy a house in the future and recently received an inheritance of ​$16,000 You intend to use your inheritance as a down payment on your house.

1. If you put your inheritance in an account that earns 7 percent interest compounded​ annually, how many years will it be before your inheritance grows to $34,000?

2.If you let your money grow for 10 years at 7 percent how much will you​ have?

3.How long will it take your money to grow to $34,000 if you move it into an account that pays 5 percent compounded​ annually? How long will it take your money to grow to $34,000 if you move it into an account that pays13 percent​?

4. What does all this tell you about the relationship among interest​ rates, time, and future​ sums

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Answer 1

(1) Initial Investment = $ 16000, Interest Rate = 7% and Target Future Value = $ 34000

Let the time required be T years

Therefore, 16000 x (1.07)^(T) = 34000

(1.07)^(T) = 2.125

T = = 11.1408 years ~ 11.14 years

(2) Intial Investment = $ 16000, Interest Rate = 7 %, Tenure = 10 Years

Future Value = 16000 x (1.07)^(10) = $ 31474.42

(3)  Initial Investment = $ 16000, Interest Rate = 5% and Target Future Value = $ 34000

Let the time required be T years

Therefore, 16000 x (1.05)^(T) = 34000

(1.05)^(T) = 2.125

T = = 15.449 years ~ 15.45 years

Initial Investment = $ 16000, Interest Rate = 13% and Target Future Value = $ 34000

Let the time required be T years

Therefore, 16000 x (1.13)^(T) = 34000

(1.13)^(T) = 2.125

T = = 6.167 years ~ 6.17 years

(4) The results of the first three sub-parts clearly show that as the interest rate goes up the time required to reach the same target future value reduces. Therefore, Interest Rates are inversely related to time with future sums remaining constant.