Question

A 20-year, $ 490,000 mortgage at 4.20\% compounded annually is repaid wit monthly payments . a. What is the size of the monthly payments ? Round to the nearest cent. b. Find the balance of the mortgage at the end of 5 years 00 Round to the nearest cent c. By how much did the amortization period shorten by if the monthly payments are increased by $ 200 at the end of year five

Answer 1

Information provided:

Mortgage= present value= $490,000

Time= 20 years*12= 240 months

Interest rate= 4.20%/12= 0.35% per month

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

PV= -490,000

N= 240

I/Y= 0.35

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

The value obtained is 3,021.20

Therefore, the size of the monthly payment is $3,021.20

b.Balance of the mortgage at the end of 5 years:

= $490,000 - ($3,021.20*5*12)

= $490,000 - $181,272

= $308,728.

c.New monthly payment= $3,021.20 + $200 = $3,221.20

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

PV= -308,728

I/Y= 0.35

PMT= 3,221.20

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

The value obtained is 116.9595.

= 116.9595/ 12= 9.75 years.

=15 years - 9.75 years= 5.25 years

Therefore, the time of the mortage will reduce by 5.25 years if the monthly payment is increased by $200.