Math

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The present value of an annuity due of $400 payable semi-annually is $5600. Interest is computed at 6% compounded semi-annually. what are the number of payments? What formula should I use for this? Thanks!

  • Math -

    sub into your Present Value formula

    PV = paym( 1 - (1+i)^-n)/i

    5600 = 400 (1 - 1.03^-n)/.03
    .42 = 1 - 1.03^-n
    1.03^-n = .58
    take log of both sides
    log(1.03^-n) = log .58
    -n(log 1.03) = log .58
    -n = log .58/log 1.03

    you do the button-pushing, I got 18.4 payments
    There will be 18 full payments of $400 plus a partial payment

  • Math -

    Thanks so much. That was my answer but that formula in my book was for ordinary annuities and I wasn't sure if it applied to annuities DUE also.

  • correction - maths -

    I did not catch the "due" part

    so I would change it to

    5600 = 400 + 400 (1 - 1.03^-n)/.03 , one 400 plus n payments
    5200 = 400 (1 - 1.03^-n)/.03
    .39 = 1 - 1.03^-n
    1.03^-n = .61
    .
    -n = log .61/log 1.03
    -n = -16.722

    n = 16.7

    So in addition to the first 400 payment we need 16 more full payments, plus a partial payment

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