# Present Value of a Perpetuity Calculator (and Growing Perpetuity)

 Rate per Period: % Growth Rate per Period: (for Growth Rate < Rate) % Annuity Payment: \$ Present Value: \$ -127,388.54

Calculates the present value of a perpetuity or the present value of a perpetual annuity or growing perpetual annuity.

## Present Value of a Perpetuity Formula:

Where pv = present value, pmt = payment, and rate = rate per period. nper = number of periods which is infinity so all other formula terms approach 0. Full present value formula can be found here.

pv = -pmt / rate

Note: leave the Growth Rate per Period blank or 0 to calculate perpetuity without growth.

Note that either the present value or payment will be a negative value.

For the default example, to yield a perpetual payment of \$10,000.00 per period at a rate of 8% per period you need a present value of -\$125,000.00. If you are putting this \$125,000.00 into an annuity then you are paying out the money in order to receive \$10,000.00 per period in the future. So the present value is negative cash flow to you and the payment value you get is positive. From the perspective of the bank or financial institution the \$125,000.00 is positive and the \$10,000.00 is negative.

## Present Value of a Growing Perpetuity Formula:

Where pv = present value, pmt = payment, rate = rate per period and growth_rate = growth rate per period for growth_rate < rate. nper = number of periods which is infinity so all other formula terms approach 0. Full present value formula can be found here.

pv = -pmt / (rate - growth_rate)

Note that either the present value or payment will be a negative value.

### **Present Value of a Perpetuity Calculations:

Rate per Period is the interest rate for each payment period. Make sure that you are consistent with the units (months, years or quarters) you use for specifying Rate per Period.