**Question 1**

A borrower is contemplating to buy a house valued at P500, 000.00 situated in Gaborone. Recently she approached a commercial bank to help finance the venture. The bank agreed to lend her 90% of the value of the house at Prime plus 2% interest rate. Prime rate currently stands at 11% and home loan interest rates are compounded yearly. Instalments on the loan will be paid at the end of each period for the next 6 years.

          **Required:**

a)      Calculate the yearly instalments to paid by the borrower
 
b)      How much in TOTAL will be paid towards interest for the entire 6 year period?
 
c)      How much of the last (6th) instalment represent principal payment?

### Problem Breakdown:
The borrower is taking a home loan to finance 90% of the house's value, which is \( P500,000 \). The loan's interest is compounded annually at the Prime rate plus 2%, and the repayment term is 6 years with yearly instalments. We are asked to find the yearly instalments, the total interest paid, and how much of the last instalment represents principal repayment.

Let's solve this step by step.

---

### Given Information:
- **House value**: \( P500,000 \)
- **Loan percentage**: 90% of house value
- **Prime rate**: 11%
- **Interest rate on loan**: Prime + 2% = 11% + 2% = 13% per annum (compounded yearly)
- **Loan term**: 6 years (instalments at the end of each year)
- **Compounding frequency**: Annually

### Part a: Calculate the Yearly Instalments

First, we need to calculate the loan amount and then use the formula for instalments on an amortizing loan.

1. **Loan amount**:
   \[
   \text{Loan amount} = 90\% \times 500,000 = P450,000
   \]

2. **Formula for instalments**:
   The formula for calculating instalments on an amortizing loan is:
   \[
   A = \frac{P \times r \times (1 + r)^n}{(1 + r)^n - 1}
   \]
   where:
   - \( A \) is the yearly instalment,
   - \( P \) is the loan amount,
   - \( r \) is the annual interest rate (as a decimal),
   - \( n \) is the number of years (loan term).

   Substituting the known values:
   \[
   P = 450,000, \quad r = \frac{13}{100} = 0.13, \quad n = 6
   \]

Let’s calculate the yearly instalment \( A \).

### Part b: Total Interest Paid

To find the total interest paid, we can compute the total amount paid over the loan term (yearly instalments × number of years) and subtract the loan principal.

Total amount paid over 6 years = \( A \times 6 \)

Total interest = Total amount paid – Loan amount

### Part c: Principal Payment in the Last Instalment

To find the portion of the last instalment that goes towards principal, we need to calculate the outstanding balance of the loan just before the final payment. The final payment will be the sum of the interest on that balance and the remaining principal.

Let me first calculate the instalments, and then proceed to the total interest and principal for the last payment.### Results:

- **Part a: Yearly Instalments**
  The yearly instalment to be paid by the borrower is approximately **P112,568.95**.

- **Part b: Total Interest Paid**
  The total interest paid over the 6-year period is approximately **P225,413.73**.

Next, we’ll calculate how much of the last (6th) instalment represents principal repayment.

To do this, we need to calculate the loan balance before the final payment, which will allow us to separate the interest and principal components of the last instalment.### Part c: Breakdown of the Last Instalment

- **Remaining balance before the last instalment**: P99,618.54
- **Interest in the last (6th) instalment**: P12,950.41
- **Principal in the last (6th) instalment**: P99,618.54

Thus, approximately **P99,618.54** of the last instalment represents principal repayment.

---

Do you have any further questions, or would you like a detailed explanation of any part?

Here are 5 related questions to consider:
1. How does the compounding frequency affect the instalment amount?
2. What would happen if the borrower made a lump sum payment during the loan term?
3. How would a change in the interest rate after 3 years impact the loan repayments?
4. What is the effect of increasing the loan term to 10 years on the total interest paid?
5. How is the amortization schedule of this loan calculated?

**Tip:** Always check if your loan allows extra payments without penalties, as it can significantly reduce the interest paid.

A borrower is contemplating to buy a house valued at P500,000.00 situated in Gaborone. Recently she approached a commercial bank to help finance the venture. The bank agreed to lend her 90% of the value of the house at Prime plus 2% interest rate. Prime rate currently stands at 11% and home loan interest rates are compounded yearly. Instalments on the loan will be paid at the end of each period for the next 6 years. Required: a) Calculate the yearly instalments to be paid by the borrower. b) How much in TOTAL will be paid towards interest for the entire 6 year period? c) How much of the last (6th) instalment represent principal payment?

Learn how to calculate the yearly instalments and total interest paid on a P450,000 home loan over 6 years at a 13% interest rate. Understand loan amortization and the breakdown of principal and interest payments. Suitable for finance students at the college level.

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