Macroeconomics help

Question

A​ variable-rate mortgage of ​$140,000 is amortized over 20 years by equal monthly payments. After 12 months the original interest rate of 8​% compounded semi-annually was raised to 8.8​% compounded semi-annually. Three years after the mortgage was taken​ out, it was renewed at the request of the mortgagor at a fixed rate of 8.6​% compounded semi-annually for a​ four-year term.

​(a) Calculate the mortgage balance after 12 months.

​(b) Compute the size of the new monthly payment at the 8.8​% rate of interest.

(c) Determine the mortgage balance at the end of the​ four-year term.

Answer 1

Hi Orick,

a. monthly payment = pr/1-(1+r)^-n

principal amount = p

monthly interest rate = r

n = number of months

interest rate, compounded semi annually = .08/6 = .0133

n = 20 years * (12 months / year) = 240 months

Solve-

monthly payment = pr/1-(1+r)^-n

140,000(.0133)/1-(1+.0133)^-240

1862/1-(.041963)

1862/.95804

monthly payment = 1943.55

In 12 months he paid: 1943.55*12 = $23,322.62

Mortgage Balance = p - 23322.62 = 140,000 - 23322.62 = $116,677.38