Florida deposited 48,000,000 shillings in a bank for three years at 4% per annum. Find the compound interest she earned if the interest is compounded every three months.

Steps to Solve

1. Determine the number of compounding periods per year Since the interest is compounded every three months (quarterly), there are 4 compounding periods in a year.

2. Calculate the interest rate per compounding period The annual interest rate is 4%, so the quarterly interest rate is $\frac{4%}{4} = 1% = 0.01$.

3. Calculate the total number of compounding periods The investment is for 3 years, and interest is compounded quarterly, therefore the total number of compounding periods is $3 \times 4 = 12$.

4. Calculate the future value of the investment Use the compound interest formula: $A = P(1 + r)^n$, where $A$ is the future value, $P$ is the principal amount, $r$ is the interest rate per period, and $n$ is the number of compounding periods. In this case, $P = 48,000,000$, $r = 0.01$, and $n = 12$. $$ A = 48,000,000(1 + 0.01)^{12} $$ $$ A = 48,000,000(1.01)^{12} $$ $$ A = 48,000,000 \times 1.12682503013 $$ $$ A = 54,087,601.45 $$

5. Calculate the compound interest earned Subtract the principal from the future value to find the compound interest. $$ CI = A - P $$ $$ CI = 54,087,601.45 - 48,000,000 $$ $$ CI = 6,087,601.45 $$