Question

Monthly payments on a $160,000 mortgage are based on an interest rate of 6.6% compounded semiannually and a 30-year amortization. If a $5000 prepayment is made along with the thirty-second payment: (Do not round the intermediate calculations.) a. How much will the amortization period be shortened? (Round Up to the next whole number.) The amortization period will be shortened by years and month(s). b. What will be the principal balance after four years? (Round your answer to two decimal places.) Balance after 4 years will be $

Answer 1

EMI = P*i*(1+i)^n/[{(1+i)^n}-1]

Where,

P = Principal = 160000

i= Interest Rate = 0.066/2 = 0.033

n= Number of periods = 30*2 = 60

Therefore, EMI = 160000*0.033*(1+0.033)^60/[{(1+0.033)^60}-1]

= 5280 *(7.01486)/[6.01486] = $6157.83

Above amount is SEMI ANNUAL PAYMENT. Monthly Payment = Above Semi Annual Payment/6 = 6157.83/6 = $1026.3

Amortization Schedule:

From above,

Amortization Period is shortened by = Original Priod - New Period = 360 months - 310 months = 50 months = 4 years and 2 months

Principal Balance after 4 years = $145077.25