Question

A ​$95,000 a mortgage is to be amortized by making monthly payments for 20 years. Interest is 7.4% compounded semi-annually for a five​-year term.

​(a)	Compute the size of the monthly payment.
​(b)	Determine the balance at the end of the five​-year term.
​(c)	If the mortgage is renewed for a five​-year term at 7​% compounded semi-annually, what is the size of the monthly payment for the renewal​ term?

​(a) The size of the monthly payment is ​$__.

​(Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as​ needed.)

​(b) The balance at the end of the five​-year term is ​$__.

​(Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as​ needed.)

​(c) The size of the monthly payment for the renewal term is $__.

​(Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as​ needed.)

Answer 1

Effective Annual Rate (EAR) = (1 + APR/n)^n - 1 = (1 + 7.4%/2)^2 - 1 = 7.54%

Monthly APR = (1 + EAR)^(1/n) - 1 = (1 = 7.54%)^(1/12) - 1 = 0.61%

Monthly Payment can be calculated using PMT function in excel

Payment = PMT(rate = 0.61%, nper = 20*12, pv = 95000, fv = 0, 0) = $753.07 .... a)

Principal Paid over 5 year period can be calculated using CUMPRINC function in excel

CUMPRINC(rate = 0.61%, nper = 240, pv = 95000, 1, 60, 0) = $12,699.92

Outstanding Balance = 95,000 - 12,699.92 = $82,300.08... b)

EAR = (1 + 7%/2)^2 - 1 = 7.12%

Monthly APR = (1 + 7.12%)^(1/12) - 1 = 0.58%

Payment = PMT(rate = 0.58%, nper = 5 x 12, pv = 82,300.08, fv = 0, 0) = $1,625.76 is the new monthly payment for 5 year term loan.