Question

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. Round to two decimal places.

A. 54,003.91
B. $2,015,88
C. $4,415.88
D. $2,040.00
E. $6,040.20

Answer 1

The question is about calculating the future value of quarterly payments compounded at an 8% annual rate over ten years.

Step-by-step explanation:

The student's question involves calculating the accumulated value of quarterly payments of $100.00 at an 8% annual interest rate, compounded quarterly, over ten years. To solve this, we use the future value formula for an annuity compounded quarterly:

FV = P × { [(1 + r)^n - 1] / r }

Where:

P = periodical payment amount = $100r = quarterly interest rate = 8% per annum / 4 = 0.02n = total number of payments = 4 payments per year × 10 years = 40

Applying these values to the formula, we get:

FV = $100 × { [(1 + 0.02)^40 - 1] / 0.02 }

Rounded to two decimal places, the future value computed indicated an accrued amount significantly higher than what would have been gained using simple interest, showing the effect of compound interest over time.