Aaron borrows a lean of $4000000 from Aspire Bank at an interest rate of 4% per annum, compounded monthly. For each successive month after the day when the loan is taken, loan interest is calculated and then a monthly instalment of $20000 is immediately paid to the bank until the loan is fully repaid. If Aaron wants to fully repay the loan after paying 300 equal instalments, find the monthly repayment correct to nearest dollar

To find the monthly repayment amount that Aaron needs to make in order to fully repay the loan after 300 instalments, we can use the formula for the monthly payment of a loan with compound interest:

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

Where:
- $ M $ is the monthly payment
- $ P = 4000000 $ is the principal loan amount
- $ r = \frac{4\%}{12} = 0.0033333 $ is the monthly interest rate
- $ n = 300 $ is the number of payments (300 months)

We will solve this equation to find the monthly payment $ M $.Aaron needs to make a monthly payment of **$21,113** to fully repay the loan in 300 instalments.

Would you like more details on the calculation or have any other questions?

Here are 8 related questions you might consider:
1. How much total interest does Aaron pay if he makes 300 instalments of $21,113?
2. What would happen to the monthly payment if the interest rate increased to 5%?
3. How much would the monthly payment be if Aaron wanted to repay the loan in 250 months instead of 300?
4. What is the outstanding balance after 150 payments?
5. How much interest is paid during the first year under this payment plan?
6. How would the monthly payment change if Aaron made bi-weekly payments instead?
7. What if Aaron decided to repay the loan in 20 years instead of 25 years?
8. How much would Aaron save in interest if he made a lump sum payment of $100,000 after 100 months?

**Tip:** When determining a loan repayment plan, it's useful to consider how shortening the loan term or making additional payments can reduce the total interest paid.

Learn how to calculate monthly loan repayments with compound interest using the formula. Solve Aaron's loan repayment problem with a detailed step-by-step solution. Includes calculation of principal, interest rate, and monthly instalments over 300 months.

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