To solve this problem, we'll use the following steps:

(a) Monthly Payment

The monthly payment for a loan can be calculated using the amortization formula:

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

Where:

• $M$ is the monthly payment
• $P$ is the loan principal (148,000)
• $r$ is the monthly interest rate (annual rate divided by 12, so $\frac{13}{100} \div 12 = \frac{0.13}{12}$)
• $n$ is the total number of payments (loan term in months, so $23 \times 12$)

(b) Interest in First Monthly Payment

Interest for the first payment is calculated by multiplying the principal by the monthly interest rate:

$\text{Interest in first payment} = P \times r$

(c) Principal in First Monthly Payment

The portion of the first payment applied to the principal is calculated by subtracting the interest from the total monthly payment:

$\text{Principal in first payment} = M - \text{Interest in first payment}$

(d) Interest in Second Monthly Payment

After the first payment, the principal decreases. So, the new interest for the second payment is calculated using the updated principal balance:

$\text{New principal} = P - (\text{Principal in first payment})$ $\text{Interest in second payment} = \text{New principal} \times r$

Now, let me calculate these values.Here are the results:

(a) Monthly payment: $1689.68
(b) Interest in the first monthly payment: $1603.33
(c) Principal applied in the first monthly payment: $86.35
(d) Interest in the second monthly payment: $1602.40

Would you like more details or have any questions?

Here are 5 related questions to expand on this topic:

1. How does increasing the interest rate impact the monthly payment and total interest paid?
2. What would happen to the monthly payment if the loan term is shortened?
3. How can you calculate the total interest paid over the entire loan period?
4. What is the principal balance after 5 years of payments?
5. How does the amortization schedule change with different payment frequencies?

Tip: Understanding how much of each payment goes toward principal versus interest can help you make informed decisions about paying off loans faster.