Answer:
To calculate the monthly payment for each option, we can use the loan formula:
Payment = (P * r) / (1 - (1 + r)^(-n))
where P is the principal amount, r is the monthly interest rate, and n is the total number of payments.
For Option A, the principal amount is $60,000, the interest rate is 4% per year, and the loan term is 10 years. We first need to convert the annual interest rate to a monthly interest rate:
r = 4% / 12 = 0.00333333 (rounded to 8 decimal places)
n = 10 years * 12 months/year = 120 months
Using the loan formula, we get:
Payment = (60000 * 0.00333333) / (1 - (1 + 0.00333333)^(-120)) = $630.55
Therefore, the monthly payment for Option A is $630.55.
For Option B, the principal amount is also $60,000, the interest rate is 3% per year, and the loan term is 20 years. We convert the annual interest rate to a monthly interest rate:
r = 3% / 12 = 0.0025 (rounded to 4 decimal places)
n = 20 years * 12 months/year = 240 months
Using the loan formula, we get:
Payment = (60000 * 0.0025) / (1 - (1 + 0.0025)^(-240)) = $342.61
Therefore, the monthly payment for Option B is $342.61.
To calculate the total amount paid over the life of the loan for each option, we simply multiply the monthly payment by the total number of payments:
For Option A, the total amount paid = $630.55 * 120 months = $75,665.92
For Option B, the total amount paid = $342.61 * 240 months = $82,226.40
To calculate the total interest paid over the life of the loan for each option, we subtract the principal amount from the total amount paid:
For Option A, the total interest paid = $75,665.92 - $60,000 = $15,665.92
For Option B, the total interest paid = $82,226.40 - $60,000 = $22,226.40
Therefore, Option A has a lower monthly payment and total amount paid over the life of the loan, but Option B has a longer loan term and a lower interest rate, resulting in a higher total interest paid over the life of the loan