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olga2289 [7]
3 years ago
13

You plan on financing a new road bike for $2,500. The bike shop offers a 13.5% APR for a 24 month loan. Use this information, an

d the table above, to determine the monthly payments. Round your answer to the nearest cent.
Mathematics
1 answer:
Mila [183]3 years ago
6 0
This question can be approached using the present value of annuity formula. The present value of annuity is given by PV=P\left( \frac{1-\left(1+ \frac{r}{t} \right)^{-nt}}{ \frac{r}{t} } \right), where: PV is the present value/amount of the loan, P is the periodic (monthly in this case) payment, r is the APR, t is the number of payments in one year and n is the number of years.

Given that the<span> financing is for a new road bike of $2,500 and that the bike shop offers a 13.5% APR for a 24 month loan.

Thus, PV = $2,500; r = 13.5% = 0.135; t = 12 payments (since payment is made monthly); n = 2 years (i.e. 24 months)

Thus,

</span>2500=P\left( \frac{1-\left(1+ \frac{0.135}{12} \right)^{-2\times12}}{ \frac{0.135}{12} } \right) \\  \\ =P\left( \frac{1-\left(1+ 0.01125 \right)^{-24}}{ 0.01125 } \right)=P\left( \frac{1-\left(1.01125 \right)^{-24}}{ 0.01125 } \right) \\  \\ =P\left( \frac{1-0.764531}{ 0.01125 } \right)=P\left( \frac{0.235469}{ 0.01125 } \right)=20.9306P \\  \\ \Rightarrow P= \frac{2500}{20.9306} =119.44
<span>
Therefore, his monthly payment is $119.44</span>
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