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14 May, 07:27

You're prepared to make monthly payments of $220, beginning at the end of this month, into an account that pays 6.3 percent interest compounded monthly. How many payments will you have made when your account balance reaches $13,000?

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  1. 14 May, 10:03
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    52 payments

    Explanation:

    A constant payment for a specified period is called annuity. The future value of the annuity can be calculated using a required rate of return.

    Formula for Future value of annuity is

    FV = P x ([ 1 + i ]^n - 1) / i

    P = Payment amount = $220

    i = interest rate = 6.3% / 12 = 0.525%

    FV = Future value = $13,000

    n = Number of payments

    $13,000 = 220 x ([ 1 + 0.525% ]^n - 1) / 0.525%

    ($13000 x 0.525%) / $220 = [ 1 + 0.525% ]^n - 1

    0.31 = [ 1 + 0.525% ]^n - 1

    0.31 + 1 = [ 1.00525 ]^n

    1.31 = 1.00525^n

    Log 1.31 = n log 1.00525

    n = Log 1.31 / log 1.00525

    n = 51.6 payments = 52 payments (rounded off to nearest whole number)
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