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Math Help - Money problem

  1. #1
    Member helloying's Avatar
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    Money problem

    Tom borrowed a sum of money at 10% per annum compound interest. If he repaid the sum only after 2 years, he would have to repay $4356. I already found the sum of money that he had borrowed to be $3600.

    The question is if he repaid the sum by two equal annual instalments, at the end of the first year and the second year, how much was each instalment?

    I didn't quite understand the question .pls teach me thanks
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  2. #2
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    Hello, helloying!

    Tom borrowed a sum of money at 10% per annum compound interest.
    If he repaid the sum only after 2 years, he would have to repay $4356.

    I already found the sum of money that he had borrowed to be $3600. Yes!

    If he repaid the sum by two equal annual installments,
    at the end of the first year and the second year,
    how much was each installment?
    This is a tricky problem . . .

    It is an Amortization problem (time payments).
    There is a formula for this situaton, but we can derive it ourselves.


    Tom owes $3600. .The bank charges 10% interest per year.
    . . Let x = amount of his two equal payments.

    During the first year, the bank charges 10% interest: . 0.10 \times 3600 \:=\:360
    . . At the end of year one, Tom owes: . 3600 + 360 \:=\:3960 dollars.

    Then Tom pays x dollars.
    . . So he owes a balance of 3960 - x dollars.


    During the second year, the bank charges 10% interest: . 0.10(3960-x)
    . . At the end of year two, Tom owes: . (3960-x) + 0.10(3960-x) dollars

    Then Tom pays x dollars and he owes $0.


    Hence: . (3960 -x) + 0.10(3960-x) \:=\:x
    . .
    [His last balance is equal to his final payment.]

    Solve for x\!:\;\;3960 - x + 396 - 0.1x \:=\:x\quad\Rightarrow\quad 4356 \:=\:2.1x

    . . x \:=\:\frac{4356}{2.1} \:=\:2074.285714... \quad\Rightarrow\quad \boxed{x \:=\:\$2074.29}

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