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

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* (15)/(100))=\$647.7`

We know that,

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

`PV\ of\ annuity=647.7,\\\\P=?,\\\\r = 14\%\ annually=(14)/(12)\%\ monthly=(14)/(1200)\ monthly\\\\n=24\ months`

Putting the values,

`\Rightarrow 647.7=P[(1-(1+(14)/(1200))^(-24))/((14)/(1200))]`

`\Rightarrow P=(647.7)/((1-(1+(14)/(1200))^(-24))/((14)/(1200)))`

`\Rightarrow P=(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* 24=\$746.4`

Then,

`\Rightarrow \text{Total payment}=\text{Down payment+Monthly payment}=(762* (15)/(100))+(746.4)=\$861`

The extra amount he will be paying,

`=861-762=\$99`