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
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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