Question

A ​$164,200 mortgage for 20 years for a new home is obtained at the rate of 5.9​% compounded monthly.

Find​

​(a) The monthly payment on the mortgage is

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

​(b) The interest in the first payment is

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

​(c) The principal repaid in the first payment is

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

​(d) The finance charge is

​(Round to two decimal places as​ needed.)

Answer 1

(a) Loan Amount = 164200

Term to repay of loan = 20 years

Annual interest rate = 5.9%

Monrhly interest rate = 0.491667%

Monthly installment = Loan Amount/PVIFA(0.4916%, 240month)

= 164200/140.7115

= $ 1166.93

(b) The interest in the first payment is = opening balance of loan * Monthly interest rate

= 164200*0.491667%

= $ 807.32

(c) The principal repaid in the first month is = Monthly installment - First interest payment

= 1166.93 - 807.32

= $ 359.61

(d) The finance charge is = Total of all interest payment which is $ 115861.69 as per loan amortization schedule which is here under

or alternatively can be calculated, Total finance charges = Monthly installment*240(months) - loan amount

= 1166.927*240 - 164200

= 280062.4 - 164200

= 115862.4 (rounding off error)

Loan Amortization schedule is as follows -

Please check with your answer and let me know.