Find the amount accumulated in the increasing annuity of $150 deposited monthly for 15 years at 5% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.
A)$4,755.83
B) $40,093.34
C) $7,609.33
D) $76,093.34
E) $18,900.00

Question

Find the amount accumulated in the increasing annuity of $150 deposited monthly for 15 years at 5% per year. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent. ​
A)$4,755.83
B) $40,093.34
C) $7,609.33
D) $76,093.34
E) $18,900.00

Quizplus · Accepted Answer

Using the formula for the future value of an increasing annuity:

FV = Pmt * [((1+r)^n - 1)/r] + PV * (1+r)^n

where:
Pmt = monthly deposit amount = $150
r = annual interest rate = 5% / 12 = 0.00416667
n = number of periods = 15 years * 12 months/year = 180 months
PV = present value (initial deposit) = $0

Plugging in the values, we get:

FV = $150 * [((1+0.00416667)^180 - 1)/0.00416667] + $0 * (1+0.00416667)^180
FV = $40,093.34

Therefore, the amount accumulated in the increasing annuity is $40,093.34. The best choice is B.

Find the Amount Accumulated in the Increasing Annuity of $150