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The value of an irregularly compounded annuity

Jamal Munshi, Sonoma State Univesity, 1992
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Example: find FV of an annuity of $500 per month for 48 months at a 5% nominal annual rate compounded daily.

1. compute the rate per compounding period

    k per day = 0.05/365 = 0.00013699

2. compute the equivalent rate per PMT period

    there are 365/12 = 30.4 days per month
    equivalent rate per month = (1+k)^n - 1
    k per month = (1.00013699)^30.4 - 1 = 0.00417507

3. now compute the FV of the annuity using 1-month periods

    FV = (PMT/k)*((1+k)^n-1)
    FV = (500/0.00417507)*((1.00417507^48-1) = $26,512