Question

A fifteen-year adjustable-rate mortgage of $117,134.80 is being repaid with monthly payments of $988.45 based upon a nominal interest rate of 6% convertible monthly. Immediately after the 60th payment, the interest rate is increased to a nominal interest rate of 7.5% convertible monthly. The monthly payments remain at $988.45, and there will be an additional balloon payment at the end of the fifteen years to pay the outstanding loan balance.

(a) Calculate the loan balance immediately after the 84th payment.

(b) Calculate the amount of interest in the 84th payment.

(c) Calculate the amount of the balloon payment

** Answer should be: (a) 77884.78 (b) 489.90 (c) $12,168.43, so the total paid at the end of fifteen years is $13,156.88

DO NOT USE EXCEL! USE FORMULA PLEASE!!!

Answer 1

(A) To calculate the loan balance we have to calculate present value of annuity (periodic payment) for first 5 year @ 6% and for another 2 @ 7.5%.

Loan amount = 117134.8

Monthly Payment is 988.45

Formula for present value annuity due is

P* ((1-(1/(1+r)ⁿ))/r)

where is

n = No of year or months

r = rate of interest

P = Periodic payment

= 988.45*((1-(1/(1+(6%/12)^(5*12)))60) + 988.45*((1-(1+(7.5%/12)^(2*12)))/24)

= 77884.78 is the loan balance after the 84th payment.

(B) Interest Amount in 84th payment is so

Balance amount in 84th payment is 78383.33 (using above formula) so the interest amount is 78383.33*(7.5%/12)

= 489.9 is the interest payment.

(C) Balloon payment is excess payment due to increase in rate of interest from 61st payment.

as per above formula of Present value

= 988.45*((1-(1/(1+(6%/12)^(5*12)))60) + 988.45*((1-(1+(7.5%/12)^(10*12)))/120)

= 104966.37 is loan amount which we have paid in 15 years now rest amount = 117134.8 - 104966.37

12168.43 is the right amount.