Question

The Taylors agreed to make monthly payments on a mortgage of​ $335 000 amortized over 15 years. Interest for the first three years was​ 3.5% compounded​ semi-annually. Determine the mortgage balance at the end of the​ three-year term.​ (Rounded to the nearest​ dollar)

A. ​$281,177.09

B. ​$284,603.06

C. ​$291,087.29

D. ​$282,909.28

Answer 1

Solution :-

Interest Rate for 6 months = 3.5% / 2 = 1.75%

Now Interest Rate per month = ( 1 + 0.0175 )^1/6 - 1

= 0.0028956

= 0.28956%

Now total monthly payments in 15 Years = 15 * 12 = 180

Amount Financed = $335,000

Now Monthly Payment = Amount Financed / PVAF ( r , n )

= $335,000 / PVAF ( 0.28956% , 180 )

= $335,000 / 140.126

= $2,390.71

Now After 3 Years Installment Remaining = ( 15 - 3 ) * 12 = 144

Now After 3 Years Balance Outstanding = $2,390.71 * PVAF ( 0.28956% , 144 )

= $2,390.71 * 117.613

= $281,177.09

Therefore Correct Answer is (a)

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