Ruth H.wants to build a house in 12 years.She estimates that the total cost will be $350,000.If she can put aside $20,000 at the end of each year,what rate of return must she earn in order to have the amount needed,assuming annual compounding?
A) Between 11% and 12%
B) Between 8% and 9%
C) 17%
D) 6.63%

Question

Quizplus · Accepted Answer

To find the rate of return required, we can use the future value formula:

FV = PV × (1 + r)^n

where FV is the future value (i.e. $350,000), PV is the present value (i.e. $0), r is the annual interest rate, and n is the number of years (i.e. 12).

We know that Ruth will contribute $20,000 at the end of each year, so we can treat this as an annuity. The future value of an annuity formula is:

FV = PMT × ((1 + r)^n - 1) / r

where PMT is the payment (i.e. $20,000), r is the annual interest rate, and n is the number of years (i.e. 12).

Substituting the values into the second formula, we get:

$350,000 = $20,000 × ((1 + r)^12 - 1) / r

Solving for r using a financial calculator or spreadsheet, we get:

r = 6.63%

Therefore, the answer is D. Ruth needs to earn a 6.63% rate of return annually to have the amount needed.

Ruth HWants to Build a House in 12 Years