Related to The Business of Life: Saving for Your First House) (Future value) You
ID: 2619024 • Letter: R
Question
Related to The Business of Life: Saving for Your First House) (Future value) 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. ?. you put your inheritance in an account hat earns 7 percent in e est compounded annuali how many years be a re our inherita ce gro 335, 00 T b. If you let your money grow for 10.25 years at 7 percent, how much will you have? c. How long will it take your money to grow to $35,000 if you move it into an account that pays 5 percent compounded annually? How long will it take your money to grow to $35,000 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 7 percent interest compounded annually, how many years will t be before your inheritance grows to $35,000? years (Round to one decimal place.) b. If you let your money grow for 10.25 years at 7 percent, how much will you have? $ (Round to the nearest cent.) How long will it take your money to grow to $35,000 if you move it into an account that pays 5 percent compounded annually? years (Round to one decimal place.) c. How long will it take your money to grow to $35,000 if you move it into an account that pays 11 percent? years (Round to one decimal place.)Explanation / Answer
a) Present value = $20000
Future Amount = $35000
Interest rate = 7%
Number of years be n
20000 * (1.07) ^ n = 35000
n = 8.23 years (Approx)
b) Present amount = $20000
Number of years = 10.5 yrs
Rate = 7%
Future amount = 20000 * (1.07)^10.5 = $40697
C) When Interest rate is 5%,
Present value = $20000
Future Amount = $35000
Number of years be n 20000 * (1.03) ^ n = 35000
n = 18.85 years
When Interest rate is 11%, Present value = $20000
Future Amount = $35000
Number of years be n 20000 * (1.11) ^ n = 35000
n = 5.34 years
d) There is a inverse relationship between both the interest rate used to compound a present sum and the number of years for which the compounding continues and the future value of that sum.