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Math Help - Maturity value

  1. #1
    Member
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    Maturity value

    Payments of $1800 and $2400 were made on a $10 000 variable-rate loan 18 and 30 months after the date of the loan. The interest rate was 11.5% compounded semiannually for the first two years and 10.74% compounded monthly thereafter. What amount was owed on the loan after three years?


    10 000 1800 2400 ?
    {________________________|_________________|______ |___|______________________|
    18 months 24months 30months 36months

    <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< >>>>>>>>>>>>>>>>>>>>>>>>>>>>
    11.5% / 2 10.74/12


    ( for the first 18 months the interest rate is 11.5% compounded semi annually after 6 months which is month number 24 the interest rate is 10.74% compounded annually )

    FV = PV ( 1 + i ) ^ n

    10 000 ( 1 + 11.5/2 ) ^ 2 * ( 1.5 )

    16 774.59

    16 774.59 - 1800 = 14 974.59

    14 974.59 ( 1 + 0.115/2 ) ^ 2 ( 0.5 )

    8 373.09

    8 373.09 ( 1 + 0.4074/12 ) ^ 0.5 * 12

    100 925.71

    100 925.71 - 2400 = 98 525.71

    98 525.71 ( 1 + 0.1074 / 12 ) ^ 0.5 * 12

    1 187 587.57

    I don't know if i did this correctly if not then where did i go wrong?
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  2. #2
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    Your second line should be  10,000\ \times\ (1+0.115/2)^3 , since it's being compounded over 3 semiannual periods (18 months).

    Similarly, the multiplier in your 5th line should be (1 + 0.115/2), as you're dealing with one 6-month compounding period.

    In both the 7th and 10th lines, there are 6 one-month compounding periods, so your multiplier on both of these lines should be  (1+0.1074/12)^6 .

    Give that a spin and check back in with what you've got.
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  3. #3
    MHF Contributor
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    If it's easier for you:
    look at it as depositing $10,000 in a savings account,
    then withdrawing $1,800 after 18 month, $2,400 after 30 months.

    Also, always look for "reasonability"; like, for this result you got:
    10 000 ( 1 + 11.5/2 ) ^ 2 * ( 1.5 )
    16 774.59

    It is impossible to earn over $6,000 after 18 months at 11.5%;
    10000 * .115 = 1150 (that's for a year!).
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  4. #4
    Member jonah's Avatar
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    You need to do a major brush up on "Order of Operations". You really should.
    Try this:

    <br />
10,000\left( {1 + \frac{{0.115}}{2}} \right)^{\left( {2 \times 2} \right)} \left( {1 + \frac{{0.1074}}{{12}}} \right)^{\left( {1 \times 12} \right)} <br />
<br />
 - 1,800\left( {1 + \frac{{0.115}}{2}} \right)^{\left( {{\textstyle{1 \over 2}} \times 2} \right)} \left( {1 + \frac{{0.1074}}{{12}}} \right)^{\left( {1 \times 12} \right)} <br />
<br />
 - 2,400\left( {1 + \frac{{0.1074}}{{12}}} \right)^{\left( {{\textstyle{1 \over 2}} \times 12} \right)} <br />

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