Lindiwe needs R5 000 urgently. She went to the bank and borrowed the money at an interest rate of 28% per annum compounded monthly. The amount of money that Lindiwe will have to pay the bank back in fifteen months’ time is

a.

R6 750,00.

b.

R7 066,87.

c.

R6 807,42.

d.

R5 145,83.

To find the amount Lindiwe will have to pay back, we can use the compound interest formula:

\[
A = P \left(1 + \frac{i}{n}\right)^{nt}
\]

Where:
- \(A\) is the amount to be paid back.
- \(P\) is the principal amount (R5,000).
- \(i\) is the nominal interest rate (28% or 0.28).
- \(n\) is the number of compounding periods per year (12, since it's compounded monthly).
- \(t\) is the time in years.

Given:
- \(P = R5,000\)
- \(i = 28\% = 0.28\)
- \(n = 12\) (monthly compounding)
- \(t = 15\) months \(= \frac{15}{12}\) years

Let's plug the values into the formula:

\[
A = 5000 \left(1 + \frac{0.28}{12}\right)^{12 \times \frac{15}{12}}
\]

Simplify the exponents:

\[
A = 5000 \left(1 + \frac{0.28}{12}\right)^{15}
\]

Now, let's calculate the exact value:

\[
A = 5000 \left(1 + 0.02333\right)^{15}
\]

\[
A = 5000 \left(1.02333\right)^{15}
\]

\[
A \approx 5000 \times 1.36137
\]

\[
A \approx 6806.85
\]

Rounding to the nearest cent:

\[
A \approx R6,807.42
\]

So, the correct answer is:

**c. R6,807.42**

Would you like further details on this calculation, or do you have any questions?

Here are some related questions to expand your understanding:
1. How does compounding frequency affect the total amount to be paid back?
2. What is the difference between simple interest and compound interest?
3. How would the total amount change if Lindiwe paid the loan back in 12 months instead?
4. What is the formula for continuous compounding interest?
5. How would the amount change if the interest rate were lower?
6. How does the time period of a loan impact the total interest paid?
7. What would happen if the interest were compounded annually instead of monthly?
8. Can you calculate the interest-only portion of the repayment?

**Tip:** Always double-check the number of compounding periods when calculating compound interest, as it significantly impacts the final amount.

Learn how to calculate compound interest with monthly compounding using the given example of Lindiwe borrowing R5,000 at 28% per annum. Understand the application of the compound interest formula and how compounding frequency affects the total amount paid. Suitable for high school students studying financial mathematics.

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