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A bank makes a 30-year fully amortizing FRM for $100,000 at an annual interest rate of...

A bank makes a 30-year fully amortizing FRM for $100,000 at an annual interest rate of 7% compounded monthly, with monthly payments.

What is the market value of this loan five years later if the annual market interest rate for this loan drops to 4%?

(Show your answer rounded to two decimal places.)

Solutions

Expert Solution

Loan Maturity = 30 years = 360 months

Loan amount = $100,000

Annual Interest Rate = 7%

Monthly interest rate = 7%/12 = 0.5833%

Monthly loan payment can be calculated using the formula

Where C is the monthly loan payment

PV is the loan amount = $100,000

i = Monthly interest rate = 0.5833%

n = loan maturity in months = 360

C = $100,000 * 0.00665302 = $665.30

Monthly loan payment = $665.30

5 years later:

Remaining Loan Maturity = 25 years = 300 months

Annual Interest Rate = 4%

Monthly interest rate = 4%/12 = 0.3333%

Monthly loan payment = $665.30

Market value of the loan can be calculated using the PV formula for ordinary annuity

Where PV is the market value of loan

C is Monthly loan payment = $665.30

i = Monthly interest rate = 0.3333%

n = Remaining Loan Maturity = 300 months

PV = $126,043.21

Market value of the loan = $126,043.21

jeff jeffy answered 2 years ago
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