Answer-
Finance charge is $99
Solution-
Price of mountain bike = $762
The store's financing requires a 15% down payment, so the present value of annuity will be,
[tex]762-(762\times \frac{15}{100})=\$647.7[/tex]
We know that,
[tex]\text{PV of annuity}=P[\frac{1-(1+r)^{-n}}{r}][/tex]
[tex]PV\ of\ annuity=647.7,\\\\P=?,\\\\r = 14\%\ annually=\frac{14}{12}\%\ monthly=\frac{14}{1200}\ monthly\\\\n=24\ months[/tex]
Putting the values,
[tex]\Rightarrow 647.7=P[\dfrac{1-(1+\frac{14}{1200})^{-24}}{\frac{14}{1200}}][/tex]
[tex]\Rightarrow P=\dfrac{647.7}{\frac{1-(1+\frac{14}{1200})^{-24}}{\frac{14}{1200}}}[/tex]
[tex]\Rightarrow P=\dfrac{647.7}{20.8277}[/tex]
[tex]\Rightarrow P=\$31.10[/tex]
With a monthly payment of this, he will be paying in 24 months will be,
[tex]=31.10\times 24=\$746.4[/tex]
Then,
[tex]\Rightarrow \text{Total payment}=\text{Down payment+Monthly payment}=(762\times \frac{15}{100})+(746.4)=\$861[/tex]
The extra amount he will be paying,
[tex]=861-762=\$99[/tex]
