Question

4) ) A mortgage balance of $137 960.70 is to be repaid over a eleven-year term by equal monthly payments at 8.1% compounded semi-annually. At the request of the mortgagor, the monthly payments were set at $1140.00. a) How many payments will the mortgagor have to make? b) What is the size of last payment? c) Determine the difference between the total actual amount paid and the total amount required to amortize the mortgage by the contractual monthly payments?

Answer 1

a. Now we have to use the present value of annuity formula to calculate the no of years

the int rate is compounded semiannually so we need to find out the int compounded monthly

(1.0405)^2 = ( 1 +r)^12

r = 0.66% ie 7.97% compounded semiannually

Present value of annuity = annuity * [ 1 - ( 1 + int rate)^ - no of years ] / int rate

137960.70 = 1140 * [ 1 - 1.0066^-n] /0.0066

lets use financial calulator to find out n

PMT = 1140

PV+- 137960.70

I/Y = 0.66

CPT < N < 605.89

No of years = 605.89 = 50.49 years

b & c

First lets calculate the present value of the monthly payments

PV = 1140*[ 1-1.0066^-11*12]/0.0066 = 100611

Difference of teh loan = 137960.7 - 100611 = 37350

last payment = future value of the idffference = 37350*( 1.0066)^12*11 = 89457