Could someone please check my math on this question involving equivalent rates?

**Funny side note: While typing this up, as a question, half way through I think I figured it out, which is why this is now a "check my math" post** :D

Hello,

I'm currently getting my grade 11 college math (Functions and Applications, MCF3M) through a learn from home program. Unfortunately I ran into a little trouble with this problem, which had me stumped :p. I would be very thankful to anyone who could check my math :)

By the way, sorry if this is not a question involving equivalent rates but it's the title of the section this is in, in my book, and I wasn't sure what it is considered. :P

Nader plans to buy a used car. He can afford to pay $280 at the end of each month for three years. The best interest rate he can find is 9.8%/a, compounded monthly. For this interest rate, the most he could spend on a vehicle is $8702.85.

Determine the amount he could spend on the purchase of a car if the interest rate is 9.8%/compounded annually.

First of all, I understand the first part about him being able to spend $8702.85. I know this can be figured out using the present value formula:

PV=R[1-(1+i)^-n]/i

=$280[1-(1+[.098/12])^-36]/(.098/12)

=8702.849629

Which, rounded, gives you $8702.85

And I think this is how you figure out the question (though like I said I'm unsure):

1) Find the (monthly?) interest rate (of the compounded annually plan?)

(1+i)^12=(1+[.098/12])

(1+i)^12=(1.008166667)

1+i=12√1.008166667

1+i=1.000678021

i=1.000678021-1

i=.000678021

2)Use this new interest rate in the present value formula used earlier

PV=R[1-(1+i)^-n]/i

=280[1-(1+.000678021)^-36]/.000678021

=9954.641382

Which, rounded, gives you $9954.64

Therefore Nate could spend $9954.64 on the purchase of a car.

*NOTE: I am also unsure whether I should be using the future value formula in step 2 instead of the present value formula.*

Like I said, if someone could look this over and tell me if I did it right or what I did wrong I would be EXTREMELY thankful! :D

- Lliam

Re: Could someone please check my math on this question involving equivalent rates?

This question has been solved here: Could someone please check my math? :)

- Lliam