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Math Help - Present value formula

  1. #1
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    Present value formula

    Here's the problem that I'm looking at just to add some context to my question:

    A borrower would like to borrow 30,000 at 8% for 5 years, but would like to pay only 2,000 for the first two years and then catch up with a higher payment for the final three years. What is the payment for the final three years?

    I understand how to solve the problem using a financial calculator. I was just wondering if there is a formula for finding the the future value of the loan after the first two years.

    I can write it out as:

    FV=(((30,000*(1.08))-2,000)*1.08)-2,000

    Which is fine if I only have to find the FV a couple years into the future.

    I know that if there were no payments, it'd simply be:

    FV=30,000(1.08^{2})

    I'm just wondering if there is a similar formula that takes payments into account.

    Thanks


    Nevermind, I found a formula. For anyone interested it's

    BAL_{k}=PV(1+i)^{k}-(PMT*\frac{(1+i)^{k}-1}{i})
    Last edited by downthesun01; May 13th 2012 at 09:56 PM.
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  2. #2
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    Re: Present value formula

    It is called a retrospective method of finding loan outstanding.
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  3. #3
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    Re: Present value formula

    Quote Originally Posted by downthesun01 View Post
    Nevermind, I found a formula. For anyone interested it's
    BAL_{k}=PV(1+i)^{k}-(PMT*\frac{(1+i)^{k}-1}{i})
    Notice that formula is a combination of 2 formulas: FV of AMOUNT less FV of PAYMENTS.
    Works like this (looking at it as 2 accounts):
    Code:
              LOAN                   SAVINGS
    YR  INT(8%)   BALANCE    PAYMENT  INT(8%) BALANCE
    0            30000.00                         .00
    1  2400.00   32400.00    2000.00     .00  2000.00
    2  2592.00   34992.00    2000.00  160.00  4160.00
    So what is owing after 2 years: 34992 - 4160 = 30832
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