Question

Jeremy received a 25 year loan of $370,000 to purchase a house. The interest rate on the loan was 4.00% compounded monthly.

a. What is the size of the monthly loan payment?

b. What is the principal balance of the loan at the end of 4 years?

c. By how much will the amortization period shorten if Jeremy made an extra payment of $54,000 at the end of the year 4? in years and moths

Answer 1

Information provided:

Mortgage= present value= $370,000

Time= 25 years*12= 300 months

Interest rate= 4.00%/12= 0.3333% per month

a.The size of the monthly payment is calculated by entering the below in a financial calculator:

PV= -370,000

N= 300

I/Y= 0.3333

Press the CPT key and PMT to compute the coupon payment.

The value obtained is 1,952.9963.

Therefore, the size of the monthly payment is $1,953.

b.Balance of the mortgage at the end of 4 years:

= $370,000 - ($1,953*4*12)

= $370,000 - $93,744

= $276,256.

c.New balance at the end year 4= $276,256 + $54,000 = $222,256.

The time of the mortgage is calculated by entering the below in a financial calculator:

PV= -222,256

I/Y= 0.3333

PMT= 1,953

Press the CPT key and N to compute the time of the mortgage.

The value obtained is 143.3264.

= 143.3264/ 12= 11.94 years.

=21 years - 11.94 years= 9.06 years

Therefore, the time of the mortgage will reduce by 9.06 years if an extra payment of $54,000 is made.

In case of any query, kindly comment on the solution.