Question

Sandra buys a new outfit, together with accessories at Edgars worth R 849. She takes the items on her Edgars account which she will repay over a term of 1 year. What is her monthly payment if interest is 23% per annum compounded monthly.

Answer 1

To calculate the monthly payment on Sandra's Edgars account for the outfit and accessories she bought, we can use the formula for the monthly payment on an amortizing loan. The formula is:

\[
M = P \frac{r(1 + r)^n}{(1 + r)^n - 1}
\]

Where:
- \(M\) is the total monthly payment.
- \(P\) is the principal amount (the loan amount).
- \(r\) is the monthly interest rate (annual interest rate divided by 12).
- \(n\) is the total number of payments (loan term in months).

Given:
- \(P = R 849\)
- Annual interest rate = 23% or 0.23
- Monthly interest rate \(r = \frac{0.23}{12} \approx 0.01916667\)
- Loan term = 1 year = 12 months, so \(n = 12\)

Now, we can plug in these values into the formula:

\[
M = 849 \cdot \frac{0.01916667(1 + 0.01916667)^{12}}{(1 + 0.01916667)^{12} - 1}
\]

First, calculate \((1 + r)^{12}\):

\[
(1 + 0.01916667)^{12} \approx 1.2492
\]

Now substitute back into the formula:

\[
M = 849 \cdot \frac{0.01916667 \cdot 1.2492}{1.2492 - 1}
\]

Calculating the numerator and the denominator:

\[
= 849 \cdot \frac{0.0239}{0.2492} \approx 849 \cdot 0.09598 \approx 81.48
\]

Thus, Sandra’s monthly payment will be approximately **R 81.48**.