Question

You are hoping to buy a house in the future and recently received an inheritance of ​$18,000. 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 ​$31,000​?

b.  If you let your money grow for 10.5 years at 9 percent​, how much will you​ have?

c.  How long will it take your money to grow to ​$31,000 if you move it into an account that pays 5 percent compounded​ annually? How long will it take your money to grow to ​$31, 000 if you move it into an account that pays 13 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 9 percent interest compounded​ annually, how many years will it be before your inheritance grows to ​$31, 000​?____ years? (round to ONE DECIMAL PLACE)

Answer 1

Answer a.

Present Value = $18,000
Future Value = $31,000
Interest Rate = 9%

Present Value * (1 + Interest Rate)^Time Period = Future Value
$18,000 * 1.09^Time Period = $31,000
1.09^Time Period = 1.722222
Time Period * ln(1.09) = ln(1.722222)
Time Period = 6.3 years

Answer b.

Present Value = $18,000
Interest Rate = 9.00%
Time Period = 10.50 years

Future Value = Present Value * (1 + Interest Rate)^Time Period
Future Value = $18,000 * 1.09^10.50
Future Value = $18,000 * 2.471600
Future Value = $44,488.8

Answer c-1.

Present Value = $18,000
Future Value = $31,000
Interest Rate = 5%

Present Value * (1 + Interest Rate)^Time Period = Future Value
$18,000 * 1.05^Time Period = $31,000
1.05^Time Period = 1.722222
Time Period * ln(1.05) = ln(1.722222)
Time Period = 11.1 years

Answer c-2.

Present Value = $18,000
Future Value = $31,000
Interest Rate = 13%

Present Value * (1 + Interest Rate)^Time Period = Future Value
$18,000 * 1.13^Time Period = $31,000
1.13^Time Period = 1.722222
Time Period * ln(1.13) = ln(1.722222)
Time Period = 4.4 years

Answer d.

There is a direct 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.