Question

John wants to buy a property for $106,250 and wants an 80 percent loan for $85,000. A lender indicates that a fully amortizing loan can be obtained for 30 years (360 months) at 6 percent interest; however, a loan fee of $3,600 will also be necessary for John to obtain the loan. Required:

a. How much will the lender actually disburse?
b. What is the APR for the borrower, assuming that the mortgage is paid off after 30 years (full term)?
c. If John pays off the loan after five years, what is the effective interest rate?
d. Assume the lender also imposes a prepayment penalty of 2 percent of the outstanding

Answer 1

The lender will disburse $81,400. The APR for the borrower is 6.17%. The effective interest rate is -6.55% if the loan is paid off after five years.

Step-by-step explanation:

To determine the disbursement amount, we subtract the loan fee from the loan amount. So, $85,000 - $3,600 = $81,400. The lender will actually disburse $81,400.

To find the APR, we need to calculate the total interest paid over the 30-year term. The monthly payment can be calculated using the formula: P = (r * PV) / (1 - (1 + r)^(-n)), where P is the monthly payment, r is the monthly interest rate, PV is the loan amount, and n is the total number of months. Plugging in the values, we get: P = (0.06/12 * $81,400) / (1 - (1 + 0.06/12)^(-360)). The monthly payment is $485.59. The APR can be calculated using the formula: APR = 12 * (1 - (1 - r)^12), where r is the monthly interest rate. Plugging in the value, we get: APR = 12 * (1 - (1 + 0.06/12)^12) = 6.17%. The APR for the borrower is 6.17%.

If John pays off the loan after five years, he will only pay interest for those five years. The remaining balance after five years can be calculated using the formula: B = PV * (1 + r)^n - P * ((1 + r)^n - 1) / r, where B is the remaining balance, PV is the loan amount, r is the monthly interest rate, n is the total number of months, and P is the monthly payment. Plugging in the values, we get: B = $81,400 * (1 + 0.06/12)^5 - $485.59 * ((1 + 0.06/12)^5 - 1) / (0.06/12) = $81,400 * (1 + 0.06/12)^5 - $441.11 = $78,719.82. The effective interest rate can be calculated using the formula: I = (B - PV) / (n * PV), where I is the effective interest rate. Plugging in the values, we get: I = ($78,719.82 - $81,400) / (5 * $81,400) = -0.0655. The effective interest rate is -6.55%.

If the lender imposes a prepayment penalty of 2% of the outstanding balance, and John pays off the loan after five years, the penalty amount would be 2% * $78,719.82 = $1,574.40. Therefore, the total amount John would need to pay off the loan would be $78,719.82 + $1,574.40 = $80,294.22.