Florida deposited sh. 48,000,000 in a bank for three years at 4% per annum. Find the compound interest she earned if the interest is compounded at every three months.
Understand the Problem
The question is asking to calculate the compound interest earned on a deposit of 48,000,000/= over three years at an annual interest rate of 4%, compounded quarterly (every three months).
Answer
The compound interest earned is approximately sh. 6,087,601.45.
Answer for screen readers
The compound interest Florida earned is approximately sh. 6,087,601.45.
Steps to Solve
- Calculate the quarterly interest rate
Since the annual interest rate is 4%, the quarterly interest rate is $\frac{4%}{4} = 1% = 0.01$.
- Calculate the number of compounding periods
The interest is compounded quarterly for 3 years, so the number of compounding periods is $3 \times 4 = 12$.
- Calculate the future value of the investment
The formula for compound interest is: $A = P(1 + r)^n$, where: $A$ is the future value of the investment/loan, including interest $P$ is the principal investment amount (the initial deposit or loan amount) $r$ is the annual interest rate (as a decimal) $n$ is the number of times that interest is compounded per year
In this case, $P = 48,000,000$, $r = 0.01$, and $n = 12$. Therefore, $A = 48,000,000(1 + 0.01)^{12}$. $A = 48,000,000(1.01)^{12}$. $A = 48,000,000 \times 1.12682503013$. $A \approx 54,087,601.45$
- Calculate the compound interest earned
The compound interest earned is the future value minus the principal. Compound Interest = $A - P$. Compound Interest = $54,087,601.45 - 48,000,000$. Compound Interest = $6,087,601.45$
The compound interest Florida earned is approximately sh. 6,087,601.45.
More Information
Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest.
Tips
A common mistake is forgetting to divide the annual interest rate by the number of compounding periods per year, or failing to multiply the number of years by the number of compounding periods per year. Another common mistake is calculating the future value correctly but forgetting to subtract the principal to find the actual compound interest earned.
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