You want to buy a new sports coupe for $84,500, and the finance office at the dealership has quoted you an APR of 5.2 percent for a 60-month loan to buy the car. a. What will your monthly payments be? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. What is the effective annual rate on this loan? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Hi, first, we need to convert this APR rate into an effective monthly rate, that is, dividing 0.052/12 =0.00433 (or 0.4333%). Then we need to use the following equation and solve for A.

[tex]PresentValue=\frac{A((1+r)^{n}-1) }{r(1+r)^{n} }[/tex]

Where:

PresentValue= 84,500

A = periodic payments (the monthly payments that you need to make)

r = 0.004333333

n=60 months

So, let´s solve for A.

[tex]84,500=\frac{A((1+0.004333333)^{60}-1) }{0.004333333(1+0.004333333)^{60} }[/tex]

[tex]84,500=\frac{0.296201791}{0.005616874} A[/tex]

[tex]84,500=A(52.73427328)[/tex]

[tex]A= 1,602.37[/tex]

Now, in order to find the effective annual rate, we need to use the following equation.

[tex]r(EffectiveAnnual)=((1+r(EffectiveMonthly))^{12} -1[/tex]

Notice that to find an effective rate you have to start with another effective rate, otherwise it won´t work. So everything should look like this.

[tex]r(EffectiveAnnual)=((1+0.004333333))^{12} -1=0.0533[/tex]

Meaning that the equivalent effective annual rate to 5.2% APR is 5.33% effective annual.

Best of luck.