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Math Help - Loan amortization

  1. #1
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    Loan amortization

    "A 30-year loan of 1000 is repaid with payments at the end of each year. Each of the first ten payments equals the amount of interest due. Each of the next ten payments equals 150% of the amount of interest due. Each of the last ten payments is X. The lender charges interest at an effective annual rate of 10%. Calculate X."

    I'm not quite sure how to solve this question. Since the first ten payments equal the amount of interest due, would it be right to assume the outstanding balance for the first ten years remain at 1000?

    The answer should be X = 97.44
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  2. #2
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    Quote Originally Posted by chewitard View Post
    "A 30-year loan of 1000 is repaid with payments at the end of each year. Each of the first ten payments equals the amount of interest due. Each of the next ten payments equals 150% of the amount of interest due. Each of the last ten payments is X. The lender charges interest at an effective annual rate of 10%. Calculate X."

    I'm not quite sure how to solve this question. Since the first ten payments equal the amount of interest due, would it be right to assume the outstanding balance for the first ten years remain at 1000?

    The answer should be X = 97.44
    Can you use a spreadsheet? I'm not seeing a good way to go about it otherwise. That second 10 years is ugly.
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  3. #3
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    Yes, 1000 is still owing after 1st 10 years.
    And yes, 97.44 is the correct payment for years 21 to 30:
    calculated (of course) using balance owing at end of 20th year.


    b = balance owing (1000.00)
    n = number of years (10)
    i = interest rate (.10)
    k = payment percentage (1.5) ...150% of interest

    Owing in n years:
    b(1 + i - ki)^n

    1000(1 + .10 - 1.5(.10))^10 = 598.7369...

    The 97.44 is then obtained from that.
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