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Number of Periods

The variable n in Time Value of Money formulas represents the number of periods.  It is intentionally not stated in years since each interval must correspond to a compounding period for a single amount or a payment period for an annuity.  

The interest rate and number of periods must both be adjusted to reflect the number of compounding periods per year before using them in TVM formulas.  For example, if you borrow $1,000 for 2 years at 12% interest compounded quarterly, you must divide the interest rate by 4 to obtain rate of interest per period (i = 3%).  You must multiply the number of years by 4 to obtain the total number of periods ( n = 8).

You can determine the number of periods required for an initial investment to grow to a specified amount with this formula:

number of periods = natural log  [(FV * i) / (PV * i)] / natural log (1 + i)

    PV = present value, the amount you invested
    FV = future value, the amount your investment will grow to
    i = interest per period

Example: You put $10,000 into a savings account at a 9.05% annual interest rate compounded annually.  How long will it take to double your investment?

LN [(20,000 * .0905) / (10,000 * .0905)] / LN (1 .0905) =

LN (2) / LN (1.0905) =.69314 / . 08663 =  8 years


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