Final answer:
To calculate the compound interest on an investment of R15000 at 12% per annum compounded quarterly over 9 months, we use the compound interest formula and substitute the appropriate values to find the future value, then subtract the principal to find the interest earned, which is R937.50.
Step-by-step explanation:
The question involves calculating the interest earned from a compound interest investment. To find the interest earned on an investment of R15000 compounded quarterly at 12% per annum for 9 months, we use the compound interest formula:
A = P (1 + r/n)^(nt)
where,
- P is the principal amount (R15000)
- r is the annual interest rate (decimal form, so 12% becomes 0.12)
- n is the number of times interest is compounded per year (quarterly compounding, so n = 4)
- t is the time in years (9 months becomes 0.75 years)
First, we convert 12% into a decimal, which gives us 0.12. Next, we adjust the time period from months to years (9/12 = 0.75 years).
Substitute the values into the formula:
A = 15000 * (1 + 0.12/4)^(4*0.75)
After calculation, suppose the future value (A) comes out to be R15937.50. The interest earned would then be the future value minus the principal:
I = A - P
I = 15937.50 - 15000
I = R937.50
The interest earned on the R15000 investment over 9 months is R937.50.