The problem involves compound interest. Aisyah is borrowing Rp. 40,000,000 to buy a motorcycle, with an interest rate of 1% per month for 1 year (12 months). We need to calculate the total amount Aisyah must repay at the end of the loan period.

The formula for compound interest is:

$A = P(1 + \frac{r}{n})^{nt}$

Where:

• $A$ = the amount to be repaid (total loan after interest),
• $P$ = principal amount (initial loan) = Rp. 40,000,000,
• $r$ = annual interest rate (since we are dealing with monthly compounding, we convert the monthly rate to an annual rate),
• $n$ = number of times interest is compounded per year (monthly compounding means 12 times per year),
• $t$ = the number of years.

Since the interest is 1% per month, it means the monthly interest rate is 0.01, and it compounds 12 times over one year.

Let’s calculate this.The total amount Aisyah must repay after 1 year, considering a 1% monthly interest rate, is approximately Rp. 45,073,001.

Would you like more details or have any further questions?

Here are 5 related questions to explore:

1. How is compound interest different from simple interest?
2. What would the total repayment be if the interest rate were 2% per month?
3. How would the repayment change if the loan duration was 2 years?
4. What would happen if Aisyah made monthly payments instead of a lump-sum repayment at the end of the year?
5. How is the total loan affected by the compounding frequency (e.g., quarterly vs. monthly)?

Tip: For loans, always check whether the interest compounds monthly, quarterly, or annually, as this significantly affects the total repayment amount.