Cindy borrowed money from a bank and she is repaying the loan by making monthly payments of R1323 at the end of every month. The loan will be paid off in 5 years and interest is calculated at a rate of 9.496% per year, compounded monthly. How much will Cindy still owe the bank immediately after making payment number 42? (Give your answer rounded to 2 decimal places. If you think the answer is R1012.3456, type in 1012.35)

To solve this problem, we need to calculate the outstanding balance on Cindy's loan after she has made 42 payments. We'll use the formula for the remaining balance of a loan, which is:

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

Where:
- \( B_n \) is the balance after \( n \) payments.
- \( P \) is the monthly payment amount.
- \( r \) is the monthly interest rate.
- \( N \) is the total number of payments.
- \( n \) is the number of payments already made.

Given:
- \( P = R1323 \)
- Annual interest rate = 9.496% (which is 0.09496 as a decimal)
- \( r = \frac{0.09496}{12} \approx 0.00791333 \)
- Total number of payments, \( N = 5 \times 12 = 60 \)
- Number of payments made, \( n = 42 \)

Now, let's calculate the remaining balance \( B_{42} \). 

First, we need to calculate the monthly interest rate and then apply the formula.The amount Cindy will still owe the bank immediately after making payment number 42 is **R464.40**.

Would you like any further details or explanations? Here are some related questions you might be interested in:

1. How is the monthly payment calculated for a loan with compound interest?
2. What happens to the outstanding balance if Cindy misses a payment?
3. How would an increase in the interest rate affect the remaining balance?
4. Can we calculate the total interest paid over the life of the loan?
5. What if Cindy decides to make an extra payment each month?

**Tip:** Always make sure to understand how interest is compounded when dealing with loans, as it significantly affects both the monthly payments and the total cost of the loan.

Learn how to calculate the remaining loan balance after making 42 payments at a compound interest rate of 9.496% per year, compounded monthly. This problem involves using the loan balance formula with monthly compounding to determine the outstanding amount owed by Cindy. Suitable for high school students studying finance and compound interest calculations.

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