Question

A bank makes a 30 year Fully Amortizing FRM for $800,000 at an annual interest rate of 4% compounded monthly, with monthly payments. What is the absolute difference between the balance and the market value of the loan after 36 monthly payments if the interest rate rises to 5%

Answer 1

$77,649.16

Step-by-step explanation:

Loan taken = $800,000

Duration of loan = 30 yrs

Interest rate = 4%

Monthly payment = PMT(RATE, NPER, PV, FV)

Rate(Monthly interest rate) = 0.33%

Nper= 360

PV=-800,000

FV = 0

Monthly payment = PMT(0.3, 03%, 360, -800,000)

Monthly payment = $3,819.32

Calculation of loan in 36 years

Monthly payment = 3,819.32

Rate = 0.33%

Years spent - 3

Yrs remaining = 27 yrs

No of month remaining = 324

Loan balance after 36 payment = Month payment (P/A, I, N)

Loan balance after 36 payment = 3,819.32 * Pv(0.33%, 324, -1,0)

Loan balance after 36 payment = $755,989.80

Market value of loan after 36 payment

Market value of loan after 36 payment = Monthly payment*(P/A, I,N)

= $3,819.32 * (P/A, 5%/12, 324)

= $678,340.64

Hence, Market value of loan after 36 payment is $678,340.64

Difference between loan balance and market value of loan = Loan balance after 36 payment - Market value of loan = $755,989.80 - $678,340.64 = $77,649.16