Present Value Factor
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This equation solves for the Present Value Factor factor, also known as the Single Payment Present Worth (SPPW) factor. The Present Value Factor approximates the fraction of the future value in an account before interest accrues due to compounded interest over some number of compounding periods, n. This assumes the initial principal is compounded to reach some future value and no additional principal is added other than the interest accrued during the period invested.
Inputs
n - number of periods compound interest is to be applied to the initial principal. Typically the periods are in months but this Present Value Factor can be computed for any integral compounding period.
i - interest rate for the compounding period. Typically the period is a month and therefore an annual rate needs to be divided by 12.
EXAMPLES
If you were to compute the Present Value Factor for a savings account which had accrued interest to reach a final amount (final principal = PFinal), and the interest rate was 4.5% annually (0.375% monthly entered as 0.00375) and the number of months the money was kept in the account was 24 months, then the Present Value Factor would be:
FactorPV =
So, the initial principal deposited was approximately 91.4% of the future value.
This example is an approximation if the compounding period is a month, since all months are not the same length. But theoretically, this can also apply on an annual compounding basis, a daily compounding basis or any integral compounding period you desire. When applied to monthly compounding it must be considered an approximation.
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