To calculate the equal monthly payments for a loan, we use the loan amortization formula:

$M = P \frac{i(1+i)^n}{(1+i)^n - 1}$

Where:

• $M$ = Monthly payment
• $P$ = Loan principal (amount borrowed)
• $i$ = Monthly interest rate (annual interest rate divided by 12)
• $n$ = Total number of payments (loan term in months)

Step 1: Identify the known values

1. The house cost is $R260,000$.
2. The buyer pays $R50,000$ in cash, so the loan principal is: $P = R260,000 - R50,000 = R210,000$
3. Annual interest rate ($r$) = 19.5%, so the monthly interest rate is: $i = \frac{19.5}{12 \times 100} = 0.01625 \, (\text{or } 1.625\% \text{ per month})$
4. Loan term = 20 years, so the total number of payments is: $n = 20 \times 12 = 240 \, \text{months}$

Step 2: Substitute values into the formula

$M = 210,000 \cdot \frac{0.01625(1+0.01625)^{240}}{(1+0.01625)^{240} - 1}$

Step 3: Compute the values step-by-step

1. $1 + 0.01625 = 1.01625$
2. $1.01625^{240}$: Calculate the compounding factor over 240 months.
3. Use the formula to find $M$.

Let me compute this for you. Given values P = 210000 # Loan principal (R) annual_interest_rate = 19.5 / 100 # Annual interest rate monthly_interest_rate = annual_interest_rate / 12 # Monthly interest rate n = 20 * 12 # Total number of payments (20 years in months)

Loan amortization formula

i = monthly_interest_rate M = P * (i * (1 + i)**n) / ((1 + i)**n - 1)

MThe monthly payment for the loan will be approximately R3,485.30.

Let me know if you need a detailed breakdown of the steps or any clarifications.

Here are 5 related questions you might find useful:

1. How is the total interest paid over the loan term calculated?
2. What happens if the interest rate changes during the loan period?
3. How does a shorter loan term affect monthly payments and total interest?
4. Can we calculate the outstanding balance after a certain number of payments?
5. What is the impact of making extra payments toward the principal?

Tip: When planning long-term loans, always consider how changes in interest rates could impact your repayment plan.