Question

A ​$85,000 mortgage is to be amortized by making monthly payments for 15 years. Interest is 3.3% compounded semi-annually for a seven-year term.

​(a)	Compute the size of the monthly payment.
​(b)	Determine the balance at the end of the seven-year term.
​(c)	If the mortgage is renewed for a seven-year term at 3% compounded semi-annually, what is the size of the monthly payment for the renewal term

Answer 1

Solution :-

Amount Financed = $85,000

Total Monthly Payments = 15 * 12 = 180

Interest rate for 6 months = 3.3% / 2 = 1.65%

Interest Rate per month = ( 1 + 0.0165 )^1/6 - 1 = 0.00273 = 0.273%

(A) Size of the monthly payment = $85,000 / PVAF ( 0.273% , 180 )

= $85,000 / 142.0439

= $598.41

(b) After 7 Years Installment remaining = ( 15 - 7 ) * 12 = 96

Balance at the end of 7th Years = $598.41 * PVAF ( 0.273% , 96 )

= $598.41 * 84.345

= $50,472.94

(c) New Interest Rate per month = ( 1 + 0.03 / 2 )^1/6 - 1 = 0.0024845 = 0.24845%

New Installments = 12 * 7 = 84

Now Monthly Installment = $50,472.94 / PVAF ( 0.24845% , 84 )

= $50,472.94 / 75.72936

= $666.49

The size of the monthly payment for the renewal term = $666.49

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