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Math Help - Basic loan calculation word problem

  1. #1
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    Basic loan calculation word problem

    I'm trying to help my son with his homework but this has me stumped; the answer is in the back of the book but I've no idea how to arrive at it.

    For this loan: ......

    principal + interest = $2835
    was repaid over a Period of 15 months
    and pays Interest at a rate of 4% per year

    What was the principal of the loan?

    Any idea what steps you would use to solve this?


    Thanks in advance
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  2. #2
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    Hello, Deutz!

    For this loan:

    Principal + Interest = $2835
    was repaid after a Period of 15 months
    and pays Interest at a rate of 4% per year

    What was the Principal of the loan?
    I assume that this is Simple Interest.


    \text{Formula: }\;A \;=\;P(1 + i)^n

    . . . \text{where: }\:\begin{Bmatrix}P &=& \text{principal} \\ i &=& \text{annual interest rate} \\ n &=& \text{number of years} \\ A &=& \text{final amount} \end{Bmatrix}


    The number of years is: . \text{15 months} \quad\Rightarrow\quad \frac{15}{12} \:=\:\frac{5}{4} \:=\:1.25\text{ years}


    \text{So we have: }\:\begin{array}{ccc} A &=& 2835 \\ i &=& 0.04 \\ n &=& 1.25 \end{array}


    \text{Substitute: }\;2835 \;=\;P(1+0.04)^{1.25} \quad\Rightarrow\quad P(1.04)^{1.25} \;=\;2835

    \text{Therefore: }\;P \;=\;\frac{2835}{(1.04)^{1.25}} \;=\;2699.363611 \;\approx\;\$269.36

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  3. #3
    MHF Contributor
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    If TRULY simple interest (no compounding):
    p + .05p = 2835.00 : 5% over 1.25 years = 4% over 1 year
    p(1.05) = 2835.00
    p = 2835 / 1.05 = 2700.00
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  4. #4
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    Thanks

    Thank you both for your replies. Much appreciated!
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