Answer to Question #248103 in Macroeconomics for Msk

Question

A new office building was constructed 5 years ago by a consulting engineering firm. At that time the firm obtained a bank loan for $100,000 with a 12% annual interest rate, compounded quarterly. The terms of the loan call for equal quarterly payments to repay the loan in 10 years. The loan also allows for its prepayment at any time without penalty. As a result of internal changes in the firm, it is now proposed to refinance the loan through an insurance company. The new loan would be for a 20-year term with an interest rate of 8% per year, compounded quarterly. The new equal quarterly payments would repay the loan in the 20-year period~ The insurance company requires the payment of a 5% loan initiation charge (often described as a "5-point loan fee"), - which will be added to the new loan.

(b) What is the difference between the equal quar terly payments on the present bank loan and the proposed insurance company loan?

Answer 1

a.

$A=\$100,000(\frac{A}{P},3\%,40)$

$=\$100,000(0.0433)\\=\$4,330$

$P=\$4,330(\frac{P}{A},3\%,20)\\=\$4,330(14.877)\\=\$64,417$

b.

Service charge =0.05P

Amount of new loan

$=1.05(\$64,417)\\=\$67,638$

Quarterly payment on new loan

$\$67,638(\frac{A}{P}, 2\%,80)\\=\$67,638(0.0252)\\=\$1,704$

Difference in quarterly payments

$=\$4,330-\$1,704\\=\$2,626$