Calculate the accumulated value of quarterly payments of $100.00 made at the end of each quarter for ten years just after the last payment has been made if interest is 8% p.a. compounded quarterly.
A) $4003.91
B) $6040.20
C) $2040.00
D) $4415.88
E) $2015.88

Question

Quizplus · Accepted Answer

Firstly, we need to calculate the number of periods (quarters) and the interest rate per quarter:

Periods = 10 years x 4 quarters per year = 40 quarters
Interest rate per quarter = 8% / 4 = 2%

Next, we can use the formula for the accumulated value of an annuity:

Accumulated value = Payment x ((1 + r)^n - 1) / r

Where:
Payment = $100.00 (the quarterly payment)
r = 2% (the interest rate per quarter)
n = 40 (the number of quarters)

Plugging in the values, we get:

Accumulated value = $100.00 x ((1 + 0.02)^40 - 1) / 0.02
Accumulated value = $6040.20

Therefore, the best choice is B) $6040.20 as this is the final accumulated value of the quarterly payments after ten years at an interest rate of 8% p.a. compounded quarterly.

Calculate the Accumulated Value of Quarterly Payments of $100