Question 9

To determine the amount of interest Leigh has paid after one year, we need to break down the total amount paid and the principal repaid.

Given:

• Principal $P = \$35,000$
• Annual interest rate $r = 4.6\%$
• Monthly payment $R = \$1529.24$
• Loan period for interest calculation = 1 year

Step 1: Convert annual interest rate to monthly rate $r_{\text{monthly}} = \frac{4.6\%}{12} = \frac{0.046}{12} \approx 0.003833$

Step 2: Calculate total payments made in one year $\text{Total payments} = 1529.24 \times 12 = 18,350.88$

Step 3: Calculate the balance after one year Using the formula for the remaining balance on an amortizing loan: $B = P \times (1 + r_{\text{monthly}})^{12} - \frac{R}{r_{\text{monthly}}} \times \left[(1 + r_{\text{monthly}})^{12} - 1\right]$

$B = 35000 \times (1 + 0.003833)^{12} - \frac{1529.24}{0.003833} \times \left[(1 + 0.003833)^{12} - 1\right]$

First, calculate $(1 + 0.003833)^{12}$: $(1 + 0.003833)^{12} \approx 1.047$

Now, calculate the balance $B$: $B = 35000 \times 1.047 - \frac{1529.24}{0.003833} \times (1.047 - 1)$

$B = 36645 - \frac{1529.24}{0.003833} \times 0.047$

$B = 36645 - 398868.81 \times 0.047 \approx 36645 - 18746.64 = 17898.36$

Step 4: Calculate the total principal repaid in one year $\text{Principal repaid} = 35000 - 17898.36 = 17101.64$

Step 5: Calculate the total interest paid in one year $\text{Total interest paid} = \text{Total payments} - \text{Principal repaid}$

$\text{Total interest paid} = 18350.88 - 17101.64 = 1249.24$

Thus, the closest answer is: $\boxed{A. \, 1253}$

Question 10

Henri is considering a 5-year interest-only loan for a car valued at $30,000 with a fixed interest rate of 8% per year compounded monthly.

Given:

• Principal $P = \$30,000$
• Annual interest rate $r = 8\%$
• Loan term = 5 years
• Time passed = 3 years

For an interest-only loan, the principal does not reduce over the life of the loan. The borrower only pays the interest periodically.

Step 1: Convert annual interest rate to monthly rate $r_{\text{monthly}} = \frac{8\%}{12} = \frac{0.08}{12} \approx 0.006667$

Step 2: Calculate the monthly interest payment $\text{Monthly interest payment} = P \times r_{\text{monthly}} = 30000 \times 0.006667 = 200$

Step 3: Calculate the total interest paid after 3 years $\text{Total interest paid in 3 years} = 200 \times 12 \times 3 = 7200$

Since this is an interest-only loan, the principal remains unchanged, so Henri would still owe the original loan amount: $\boxed{E. \, 30000}$

Would you like more details or have any questions?

Here are 8 related questions:

1. What is the difference between an interest-only loan and an amortizing loan?
2. How does compounding frequency affect the total interest paid on a loan?
3. What would be the monthly payments for a fully amortizing loan of $30,000 at 8% over 5 years?
4. How do you calculate the remaining balance on an amortizing loan?
5. How can you determine the total interest paid over the life of a loan?
6. What are the advantages and disadvantages of an interest-only loan?
7. How does the interest rate impact the monthly payment on a loan?
8. Can you explain how the formula for the annuity payment $R$ is derived?

Tip: When dealing with interest-only loans, remember that the principal remains the same throughout the loan period, and only the interest is paid periodically.