Question

nterest for the initial 4-year term of a $105 000 mortgage is 4.39% compounded semi-annually. The mortgage is to be repaid by equal weekly payments over 20 years. The mortgage contract permits lump-sum payments at each anniversary date up to 10% of the original principal. (a) What is the balance at the end of the 4-year term if a lump-sum payment of $7000 is made at the end of the third year? no change in the interest rate? is made? (b) How many more payments will be required after the 4-year term if there is (c) What is the difference in the cost of the mortgage if no lump-sum payment

Answer 1

let "n" be the no. of years of mortgage and "i" be the interest on such mortgage

given:

n= 4 years and i= 4.39% p.a.

now, since the interest is being paid semi annually, we will double the "n" and reduce the "i" to half

i.e. , n=8 years and i= 2.195%p.a.

(a) in this part, the amount of interest and principal paid upto 3 years would be = (2.195% x 6years x 150000) + {(150000/20)x3years} =$42,225.

total amount of interest and principal to be paid = 150000+ (150000 x 2.195% x 8years)= 176,340$

now, amount outstanding at the end of third year would be $176,340 - $42,225 - $7000=127,115$

(b) if the interest rate remains constant, then after third year, there will be 2 more interest payments and principal amount will be continued to be paid for the remaining 17 years in weekly installments.

(c) if no lump sum payment was made, then mortgage would have been repaid weekly for the next 17 years at $144.230 per week. instead, it will now be paid at $136.312 per week.