You make 6 quarterly deposits starting at $135 and increasing at a constant rate of 4.5%. The interest rate is 8.4% compounded quarterly. What is the size of the last deposit?

Question

Quizplus · Accepted Answer

We can solve this problem using the formula for the future value of an annuity:

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

where PMT is the quarterly deposit amount, r is the quarterly interest rate, and n is the number of quarters. We can use algebra to solve for the PMT, given the other variables:

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

We know that the first deposit is $135, and each subsequent deposit increases by a constant rate of 4.5%. Therefore, the second deposit is:

$135 * 1.045 = $141.98

The third deposit is:

$141.98 * 1.045 = $149.10

And so on, until we reach the sixth and final deposit, which we'll call X. To find X, we need to solve for the future value of the annuity using the above formula, and then solve for X using the second formula:

FV = $135 + $141.98 + $149.10 + $156.37 + $163.89 + X
r = 0.084 / 4 = 0.021
n = 6

FV = X * ((1 + 0.021)^6 - 1) / 0.021 = $827.21
X = $827.21 / ((1 + 0.021)^6 - 1) * 0.021 = $168.23

Therefore, the size of the last deposit is $168.23. The answer is B.

You Make 6 Quarterly Deposits Starting at $135 and Increasing