A principal of R1 760.00 is invested for 2.25 years at a rate of 6.25% per annum compounded bi-annually. Determine what the investment will amount to at the end of the term and how much interest will be earned.

Question

R1886.17


R2312.03


R2021.39


R2017.22


None of the above

Answer 1

To calculate the investment amount at the end of the term, we can use the formula for compound interest:

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

Where:
A = the amount of money accumulated after n years, including interest
P = the principal amount (the initial amount of money)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the time the money is invested for in years

In this case:
P = R1 760.00
r = 6.25% = 0.0625
n = 2 (since it is compounded bi-annually)
t = 2.25 years

A = R1 760.00(1 + 0.0625/2)^(2*2.25)
A = R1 760.00(1 + 0.03125)^(4.5)
A = R1 760.00(1.03125)^(4.5)
A = R1 760.00(1.160394)
A = R2 042.62

The investment will amount to R2 042.62 at the end of the term.

To calculate the amount of interest earned, we subtract the principal from the total amount:

Interest = R2 042.62 - R1 760.00
Interest = R282.62

Therefore, the amount of interest earned will be R282.62.

None of the above options match the correct answer, but the correct answer is R282.62.