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

  1. #1
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    Smile 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**

    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 . 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!

    - Lliam
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  2. #2
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    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
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