Ken just purchased new furniture for his house at a cost of $15,000. The loan calls for weekly payments for the next 5 years at an annual interest rate of 10.15 percent. How much are his weekly payments?

Multiple Choice

$77.30

$57.69

$73.62

$76.39

$76.07

To calculate Ken's weekly payments, we can use the formula for the **payment amount** on a loan, which is given by the formula for the **annuity payment**:

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

Where:
- $ P $ is the loan amount ($15,000),
- $ r $ is the interest rate per period (weekly),
- $ n $ is the total number of payments.

### Step 1: Determine the values
- **Loan Amount (P)**: $15,000.
- **Annual Interest Rate**: 10.15%, so weekly interest rate $ r $ is $ \frac{10.15\%}{52} = \frac{0.1015}{52} = 0.001952 $ (since there are 52 weeks in a year).
- **Loan Term**: 5 years, which is 5 × 52 = 260 weeks.

### Step 2: Plug the values into the formula
Now, let's calculate the weekly payment using the formula.

\[
PMT = \frac{15,000 \times 0.001952}{1 - (1 + 0.001952)^{-260}}
\]

I'll calculate this now.Ken's weekly payment is approximately **$73.62**.

The correct answer is **$73.62**.

Would you like further details or explanations on how this was calculated? 

Here are 5 related questions you might find useful:
1. How does increasing the loan term affect the weekly payments?
2. How would the payments change if the interest rate were lower?
3. What if Ken wanted to pay off the loan in 3 years instead of 5?
4. How do different compounding periods (weekly, monthly, etc.) impact loan payments?
5. What happens if Ken makes extra payments on the loan?

**Tip:** The longer the loan term, the smaller each payment, but you'll end up paying more in interest over time.

Ken just purchased new furniture for his house at a cost of $15,000. The loan calls for weekly payments for the next 5 years at an annual interest rate of 10.15 percent. How much are his weekly payments? Multiple Choice: $77.30, $57.69, $73.62, $76.39, $76.07

Learn how to calculate weekly payments on a $15,000 loan over 5 years with a 10.15% interest rate using the annuity payment formula. This detailed explanation covers key financial concepts like interest rates and loan repayment. Suitable for financial math students and loan repayment calculations.

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