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Thread: Calculating the actual cost of a loan

  1. #1
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    Calculating the actual cost of a loan

    Hey guys, got a math problem here. Teacher didn't give us anything on how to do it, and algebra was years ago. Here is the problem:

    "Dimitri wants to buy a stereo for 650 dollars and pay for it using a credit card that has an Annual Percentage Rate of 19.8% and a periodic interest rate of 1.65%. Dimitri pays a minimum monthly payment of $21.45"


    Question 1: How long will it take him to pay for the stereo?
    Question 2: What is the total amount Dimitri will pay for the stereo?
    Question 3: What is Dimitri's total cost of using credit?

    I have no idea where to even start. Thanks.
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  2. #2
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    Re: Calculating the actual cost of a loan

    Quote Originally Posted by HeyAwesomePeople View Post
    Hey guys, got a math problem here. Teacher didn't give us anything on how to do it, and algebra was years ago. Here is the problem:

    "Dimitri wants to buy a stereo for 650 dollars and pay for it using a credit card that has an Annual Percentage Rate of 19.8% and a periodic interest rate of 1.65%.
    These are not separate pieces of information. The annual rate is 19.8% so the monthly rate is 1.65%.

    Dimitri pays a minimum monthly payment of $21.45"
    The first month he pays 1.65% of 650= $10.73 (rounded up to the nearest penny) interest so he actually paid 21.45- 10.73= $10.73 toward the principle, leaving 650- 10.73= 639.27 still to be paid. The second month he paid 1.65% of 639.27= $10.55 interest so he actually paid 21.45- 10.55= $10.90 toward the principle leaving 639.27- 10.90= $628.37 still to be paid. The third month he paid 1.65% of 628.37= $10.37 interest so he actually paid 21.45- 10.37= $11.08 toward the principle leaving 628.37- 11.08= 617.29 still to be paid.

    Continue that until the principle is paid off.

    Question 1: How long will it take him to pay for the stereo?
    Question 2: What is the total amount Dimitri will pay for the stereo?
    Question 3: What is Dimitri's total cost of using credit?

    I have no idea where to even start. Thanks.
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  3. #3
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    Re: Calculating the actual cost of a loan

    Quote Originally Posted by HeyAwesomePeople View Post
    "Dimitri wants to buy a stereo for 650 dollars and pay for it using a credit card that has an Annual Percentage Rate of 19.8% and a periodic interest rate of 1.65%. Dimitri pays a minimum monthly payment of $21.45"
    Formula for loan payment calculation:
    p = a*i / [1 - 1/(1+i)^n]
    With your problem:
    p = 21.45
    a = 650.00
    i = .0165
    n = ?

    In terms of n, formula becomes:
    n = LOG[p / (p - a*i)] / LOG(1 + i)

    Do the maths and you'll find that when n=42,
    7.52 remains owing; so a small 43rd payment remains.

    If payment was 21.58, then n=42 would result in zero owing.

    If you're still stuck, then you need classroom help:
    not provided here.
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