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Math Help - interest formulas

  1. #1
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    interest formulas

    I was looking for a strategy for a problem I was working on

    A car may be purchased with a 3k downpayment now and 60 month payments of 280. If the interest rate is 12% compounded monthly, what is the price of the car?

    I know that 12% is the nominal rate and that you have to divide 12% by 12 months to get 1% interest per month.

    So do I find the effective rate and than apply that interest rate to the 5 years of payments made?
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  2. #2
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    Quote Originally Posted by jason03 View Post
    A car may be purchased with a 3k downpayment now and 60 month payments of 280. If the interest rate is 12% compounded monthly, what is the price of the car?
    3000+280a_{\overline{60|}}

    That annuity is priced using 12% compounded monthly, or 1.12^{\frac{1}{12}} -1 = .009488793 \rightarrow i^{(m)} interest.

    a_{\overline{60|}} = \frac{1-v^{60}}{i^{(m)}}
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  3. #3
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    so your saying that the interest per month over the 5 year period is just under 1%?...

    Is that considering compounding?

    Thanks
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  4. #4
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    Hello, Jason!

    We're expected to know the Amortization Formula

    . . A \;=\;P\cdot\frac{i(1+i)^n}{(1+i)^n-1} \qquad \text{where}\:\begin{Bmatrix}A &=& \text{periodic payment} \\ P &=& \text{principal borrowed} \\ i &=& \text{periodic interest rate} \\ n &=& \text{number of periods} \end{Bmatrix}


    A car is purchased with a $3,000 downpayment and 60 monthly payments of $280.
    If the interest rate is 12% compounded monthly, what is the price of the car?
    We will use this variation: . P \;=\;A\cdot\frac{(1+i)^n-1}{i(1+i)^n}

    We have: . A = 280,\;i \:=\:\frac{12\%}{12} \:=\:0.01,\;n \,=\,60

    Hence: . P \;=\;280\cdot\frac{1.01^{60} - 1}{(0.01)(1.01)^{60}} \;=\;12587.41075


    Therefore, the amount of the loan is \$12,587.41

    . . and the price of the car is: . \$12.587.41 + 3,000 \;=\;\$15,587.41
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  5. #5
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    Thanks!,..Im studying Mechanical Engineering and am taking my first Engineering Economic Analysis Class. Im very rusty with finance and economics so thanks again.
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