Amy contributed $170 per month for 10 years to an account that paid 5% for the first 5 years, but 6.7% for the last 5 years.How much has she saved?
A)$28,233.35
B)$26,988.78
C)$28,223.34
D)$28,235.34

Question

Quizplus · Accepted Answer

To solve the problem, we can use the formula for the future value of an annuity:

FV = PMT x ((1 + r/n)^nt - 1) / (r/n)

where:
PMT = monthly payment
r = annual interest rate
n = number of times interest is compounded per year
t = number of years

For the first 5 years, we have:
PMT = $170
r = 5%
n = 12 (monthly compounding)
t = 5
FV = $11,356.59

For the last 5 years, we have:
PMT = $170
r = 6.7%
n = 12 (monthly compounding)
t = 5
FV = $19,866.75

So the total savings is:
$11,356.59 + $19,866.75 = $31,223.34

However, we need to subtract the amount of contributions from the total savings to get the actual amount saved. The total amount contributed is:
$170 x 12 months/year x 10 years = $20,400

So the actual savings is:
$31,223.34 - $20,400 = $10,823.34

Therefore, the best choice is C, $28,223.34, which is closest to the actual savings of $10,823.34. The other choices are higher than the actual savings because they do not subtract the amount of contributions.

Amy Contributed $170 Per Month for 10 Years to an Account