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What would be the **payments** of the first option?

Select one:

a.

R 900.00


b.

R 400.00

c.

R 500.00


d.

R 300.00

To calculate the **payments** for Option 1, we need to understand that it represents a future value calculation involving an installment loan or investment. We are given the following information for Option 1:

- **Nominal Rate**: 16.3%
- **Interest periods per year**: 12
- **Duration**: 3 years
- **Surround Sound System Price**: R8,500.00 (which can be considered as the present value or loan amount)
- **Possible Deposit**: R2,000.00

### Step 1: Subtract the deposit from the total price
First, subtract the deposit from the total price of the sound system:

\[
\text{Present Value (loan amount)} = 8,500.00 - 2,000.00 = R6,500.00
\]

### Step 2: Convert nominal interest rate to monthly rate
The nominal interest rate is 16.3% annually. We need to convert this to a monthly interest rate because there are 12 interest periods per year:

\[
\text{Monthly Interest Rate} = \frac{16.3\%}{12} = \frac{0.163}{12} = 0.01358333
\]

### Step 3: Total number of payments
The loan duration is 3 years, and since there are 12 interest periods per year, the total number of payments is:

\[
\text{Total Payments} = 3 \times 12 = 36
\]

### Step 4: Calculate monthly payments
Using the loan payment formula for fixed monthly payments:

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

Where:
- \( P = 6,500 \) (loan amount)
- \( r = 0.01358333 \) (monthly interest rate)
- \( n = 36 \) (total number of payments)

Now let's compute the monthly payment.The monthly payment for Option 1 is approximately **R 229.48**.

Since this value doesn't exactly match any of the provided options, it is likely that the nearest rounded value would be **R 300.00** (option d).

Would you like further clarification on the calculations, or do you have any other questions?

Here are 5 related questions to consider:
1. How does the deposit affect the loan amount?
2. What is the difference between nominal and effective interest rates?
3. How would the monthly payment change with a different interest rate?
4. What happens if the duration of the loan is extended?
5. How is the monthly interest rate calculated from the nominal rate?

**Tip**: Always round payment amounts carefully, as slight differences can arise from rounding the interest rate or time periods.

What would be the **payments** of the first option?

Learn how to calculate the monthly loan payment for purchasing a sound system priced at R8,500.00 with a 16.3% nominal interest rate over 3 years. This example covers essential concepts of loan amortization, monthly interest rates, and payment schedules.

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