The Chavez family has decided to save up for a new spa. They want to save $10,000 in five years. They find a savings account for which interest was compounded monthly at 8.2%. How much will they have to deposit each month to meet this goal?
A) $54
B) $97
C) $135
D) $256

Question

Quizplus · Accepted Answer

We can use the formula for future value of an annuity to calculate the monthly deposit needed.

FV = PMT * [(1 + r/n)^(nt) - 1]/(r/n)

Where:
FV = future value (which is $10,000 in this case)
PMT = monthly deposit we need to find
r = annual interest rate (8.2%)
n = number of times interest is compounded per year (12 for monthly)
t = number of years (5)

Plugging in the values, we get:

10,000 = PMT * [(1 + 0.082/12)^(12*5) - 1]/(0.082/12)

Solving for PMT gives us:

PMT = 135.14

Rounding up to the nearest dollar, the monthly deposit needed is $135. Therefore, the best choice is (C).

The Chavez Family Has Decided to Save Up for a New