27.07.2022 - 13:15

# Suppose you have just spoken to a bank about borrowing $100,000 to purchase a house, and the loan officer has told you that a$100,000 loan, to be repaid in monthly installments over 15 years with an interest rate of 0.6% per month, could be arranged. If

Question:

Suppose you have just spoken to a bank about borrowing $100,000 to purchase a house, and the loan officer has told you that a$100,000 loan, to be repaid in monthly installments over 15 years with an interest rate of 0.6% per month, could be arranged. If the bank charges a loan initiation fee of $600, a house inspection fee of$400, and 1 point, what is the effective annual interest rate of the loan being offered?

• The effective annual interest rate of the loan being offered is 8.09%. To calculate the effective annual interest rate, we need to first determine the total cost of the loan. The loan initiation fee of $600 and the house inspection fee of$400 add up to $1,000. One point on a$100,000 loan is equal to 1% or $1,000, so the total cost of the loan is$2,000. Next, we need to calculate the monthly payment. Using the loan amount, interest rate, and loan term, we can use a loan amortization calculator to find out that the monthly payment is $968.03. To calculate the annual interest rate, we need to use the effective annual rate formula: (1 + r/m)^m - 1, where r is the interest rate per period, and m is the number of compounding periods per year. In this case, r is 0.6% per month, which is equivalent to 7.2% per year (0.6% x 12 months). The loan is repaid over 15 years, which means there are 180 monthly payments, or 12 compounding periods per year. Plugging in these values, we get: (1 + 0.072/12)^12 - 1 = 0.081 or 8.1% Finally, we subtract the total cost of the loan ($2,000) from the loan amount ($100,000) to get the net loan amount ($98,000) and plug it into the effective annual rate formula: (1 + 0.081)^1 - 1 = 0.0809 or 8.09% Therefore, the effective annual interest rate of the loan being offered is 8.09%.
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