You want to save $710 per quarter for 15.5 years towards the purchase of a motor home. You think that you can earn 6.56% compounded quarterly for this period of time. If your first deposit is in 3 months, what is the most expensive motor home that you will be able to purchase?
A) $44 020.00
B) $75 999.79
C) $75 399.79
D) $27 501.82
E) $79 999.79

Question

Quizplus · Accepted Answer

To find out the maximum purchase price, we need to calculate the future value of the savings over the 15.5 year period. Using the formula for compound interest:

FV = PV × (1 + r/n)^(nt)

Where:
PV = present value (the first deposit)
r = annual interest rate
n = number of times compounded per year
t = time in years

PV = $710
r = 6.56% = 0.0656
n = 4 (compounded quarterly)
t = 15.5

FV = $710 × (1 + 0.0656/4)^(4 × 15.5)
FV = $710 × 1.5384^62
FV = $75,399.79 (rounded to nearest cent)

Therefore, the most expensive motor home that can be purchased is $75,399.79.

Note: Choice B is close to the correct answer, but it is slightly higher due to rounding.

You Want to Save $710 Per Quarter for 15