Final answer:
To calculate the monthly PI payment for a $60,000 loan at a 10% interest rate with a factor of 8.78, you multiply the loan amount by the factor and divide by 12.
The monthly PI calculated in this manner is not realistic since it is less than the monthly interest accrued, indicating an error in the calculation or the factor given.
Step-by-step explanation:
The student has asked how to calculate the monthly principal and interest (PI) payment for a $60,000 loan with a 10% interest rate over a 30-year term, given a factor of 8.78.
Additionally, the student wants to know the amount of the first payment's principal and interest. Using the factor, the monthly PI can be calculated by multiplying the loan amount by the factor.
To determine how much of the first payment goes toward the principal and how much goes to interest, it's necessary to calculate the interest for the first month and subtract it from the total monthly payment.
The monthly PI payment for the $60,000 loan is calculated as follows: $60,000 × 8.78 factor = $5,268 per year. Dividing by 12 months gives $439 per month.
Assuming the same interest rate applies throughout, the first month's interest would be $60,000 × 10% × (1/12) = $500. Since the monthly payment is $439, the remaining amount would not be enough
hence this scenario would need adjusting as a loan cannot have a monthly payment less than the interest accrued unless it is a negatively amortizing loan.