A principal of R1 700.00 is invested for 2.5 years at a rate of 6.5% per annum compounded quarterly. Determine what the investment will amount to at the end of the term and how much interest will be earned.

Answer 1

First, we need to calculate the interest earned for each quarter using the formula:

A = P(1 + r/n)^(nt)

Where:
A = the amount of money accumulated after n years, including interest.
P = the principal amount (R1 700.00 in this case).
r = annual interest rate (6.5%).
n = number of times the interest is compounded per year (4 for quarterly).
t = number of years the money is invested for (2.5 years).

Calculating the interest earned for each quarter:
r = 6.5% = 0.065
n = 4
t = 2.5

A = R1 700.00(1 + 0.065/4)^(4*2.5)
A = R1 700.00(1 + 0.01625)^10
A = R1 700.00(1.01625)^10
A = R1 700.00(1.17264060085)
A = R1 997.48

The investment will amount to R1 997.48 at the end of the term.

Now, calculate the interest earned:
Interest = A - P
Interest = R1 997.48 - R1 700.00
Interest = R297.48

Therefore, the interest earned will be R297.48.