This question can be approached using the present value of annuity formula. The present value of annuity is given by [tex]PV=P\left( \frac{1-\left(1+ \frac{r}{t} \right)^{-nt}}{ \frac{r}{t} } \right)[/tex], 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 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,
[tex]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[/tex]
Therefore, his monthly payment is $119.44
