Final answer:
Compound interest for R 15,625 at a quarterly compounded rate of 16% per annum over 9 months is computed using the compound interest formula, with adjustments for quarterly rates and periods.
Step-by-step explanation:
The question concerns the calculation of compound interest on an initial principal amount of R 15,625 when the interest is compounded quarterly at an annual rate of 16% over a period of 9 months. To compute compound interest in such a scenario, we must apply the compound interest formula:
A = P(1 + r/n)nt,
where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (in decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.
For a quarterly compounding period, the rate and time should be adjusted to a quarterly basis. The quarterly rate is 16% divided by 4, and since 9 months is three-quarters of a year, the time period t is 0.75 years. Using this information, we calculate the compound interest earned over the given period.
It's important to note that compound interest can considerably impact the total amount accrued over time, especially with larger sums and prolonged investment periods - a key concept in financial mathematics.