Question

Part 1 of 3Suppose that on January 1 you have a balance of $4500 on a credit card whose APR is 12%, which you want to pay off in 1 year. Assume that you make no additional charges to the card after January 1,a. Calculate your monthly paymentsb. When the card is paid off, how much will you have paid since January 1?c. What percentage of your total payment from part(b) is interest?Part 1: The monthly payment is ?(Do not round unti the final answer. Then round to the nearest cont as needed.)

Answer 1

Step 1 - write out the formula for computing the monthly payment d

`P_0=(d(1-(1+(r)/(k))^(-Nk)))/(((r)/(k)))`

Where

`\begin{gathered} P_0=\text{ the balance on the credit} \\ d=\text{ the monthly payment} \\ r=\text{ The APR, the annual percentage rate} \\ k=\text{ the number of payments in a year} \\ N=\text{ the number of years} \end{gathered}`

Step 2 - write out the given values and substitute them into the formula:

In this case,

`P_0=4500,d=?,r=12\text{ \%=0.12},k=12,N=1`

Therefore,

`4500=(d(1-(1+(0.12)/(12))^(-0.12)))/((0.12)/(12))`

Dividing the numbers, we have

`4500=(d(1-(1+0.01)^(-0.12)))/(0.01)`

Multiplying both sides by 0.01, we have:

`\begin{gathered} 45=d(1-(1+0.01)^(-0.12)) \\ \text{Hence} \\ 45=d(1-1.01^(-0.12)) \end{gathered}`

Therefore,