Question

Katie Cole purchased a mountain bike with an installment loan that has an APR of 14%. The mountain bike sells for $762. The store's financing requires a 15% down payment and 24 monthly payments. What is the finance charge? (Wait until the end of your calculations to round your answer.)

Answer 1

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,

$762-(762\times \frac{15}{100})=\ 647.7$

We know that,

$\text{PV of annuity}=P[\frac{1-(1+r)^{-n}}{r}]$

$PV\ of\ annuity=647.7,\\\\P=?,\\\\r = 14\%\ annually=\frac{14}{12}\%\ monthly=\frac{14}{1200}\ monthly\\\\n=24\ months$

Putting  the values,

$\Rightarrow 647.7=P[\dfrac{1-(1+\frac{14}{1200})^{-24}}{\frac{14}{1200}}]$

$\Rightarrow P=\dfrac{647.7}{\frac{1-(1+\frac{14}{1200})^{-24}}{\frac{14}{1200}}}$

$\Rightarrow P=\dfrac{647.7}{20.8277}$

$\Rightarrow P=\ 31.10$

With a monthly payment of this, he will be paying in 24 months will be,

$=31.10\times 24=\ 746.4$

Then,

$\Rightarrow \text{Total payment}=\text{Down payment+Monthly payment}=(762\times \frac{15}{100})+(746.4)=\ 861$

The extra amount he will be paying,

$=861-762=\ 99$