Niki pays $39,467 interest will he have paid in total, to pay off his loan of $61,600 with an interest rate of 9.84%.
It is the value in the present of a sum of money, in contrast to some future value it will have when it has been invested at compound interest.
It is given that,
Niki makes the same payment every two months to pay off his $61,600 loan.
Interest rate(r)=9.84%
If Niki pays off his loan after exactly eleven years.
We have to determine,
Interest pay in total=?
According to the question,
Total interest is determined by:
[tex]\text{PV}=\dfrac{\text{P}\times({1-\dfrac{1+r}{t}^{-nt})}}{\dfrac{r}{t}}}[/tex]
where,
PV = $61,600,
r = interest rate = 9.84% = 0.0984;
t = number of payments in a year = 6;
n = number of years = 11 years and P is the periodic payment.
Substitute all the values in the above formula,
[tex]\text{PV}=\dfrac{\text{P}\times[({1-\dfrac{1+r}{t})^{-nt}]}}{\dfrac{r}{t}}}\\\\\text{61,600}=\dfrac{\text{P}\times[({1-\dfrac{1+0.0984}{6})^{-11\times6}]}}{\dfrac{0.0986}{6}}}\\\\\rm {61,600\times0.0164}=P\times(1-0.341769)\\\\1010.24=0.658231P\\\\P=1534.78[/tex]
Therefore,
Niki pays $1,534.78 every 2 months for 11 years,
The total payment made by Niki:
[tex]11\times 6\times\$ 1,534.78 = \$101,295.48[/tex]
Therefore, interest paid by Niki:
[tex]\$101,295.48 - \$61,600 = \$39,695.48.[/tex]
Hence, Niki pays $39,467 interest will he have paid in total. So option D is correct.
Learn more about present value, refer:
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