question archive You are hoping to buy a house in the future and recently received an inheritance of ?$16,000
You are hoping to buy a house in the future and recently received an inheritance of ?$16,000
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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.
a. If you put your inheritance in an account that earns 9 percent interest compounded? annually, how many years will it be before your inheritance grows to ?$34,000??
b. If you let your money grow for 9.5 years at 9 percent?, how much will you? have?
c. How long will it take your money to grow to ?$34,000 if you move it into an account that pays 3 percent compounded? annually? How long will it take your money to grow to ?$34,000 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?
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a. No. of years = Ln($34,000 / $16,000) / Ln(1 + 9%)
= 8.75 years
b. Amount = $16,000 * (1 + 9%)9.5
= $165680
c. No. of years = Ln($34,000 / $16,000) / Ln(1 + 3%)
= 25.50 years
No. of years = Ln($34,000 / $16,000) / Ln(1 + 11%)
= 7.22 years
d. Future sum increases with the increase in interest rate or time.
- Any fall in the interest rate would lower future value, with an increase in the holding period will increase future value.
- Reducing the interest rate reduce the future value factor and ultimately the future value.
- Increasing the holding period increases the future value factor and thus future value.
