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# Present Value of a Graduated Annuity Due Calculator

This Formula Calculator calculates the present value of series of payment that increase at a constant rate with the first payment at the beginning of period 0.

Formula: pv((1 + fcRate / 100) / (1 + fcGrowth / 100) - 1, fcnper, fcpmt, 0, 1)

PV / fcPv : The present value.
N / fcNper : The number of periods.
i% / fcRate : The periodic rate.
PMT / fcPmt : The base periodic payment at the beginning of period zero. This payment increases by g% each period.
g% / fcGrowth : The periodic growth rate of the payment.

## Example 1

"You are considering the purchase of an investment that will pay \$1,000 immediately, and then 4 additional payments that grow at a rate of 3% per year to account for expected inflation. If your required return is 8% per year, what is the value of this investment?"
(Graduated Annuities Using Excel - TVMCalcs.com)

Value Keystrokes Display Description
5 N 5.00 Stores the N value.
8 i% 8.00 Stores the i% value.
1000 PMT 1,000.00 Stores the PMT value.
3 g% 3.00 Stores the g% value.
PV -4,557.98 Calculates the present value.

## Example 2

If you are able to purchase the investment for \$4,500, what would your return be?

Value Keystrokes Display Description
-4500 PV -4,500.00 Stores the PV value.
i% 8.73 Calculates the periodic rate.

## Reference:

Graduated Annuities Using Excel - TVMCalcs.com

Graduated Annuities on the HP 12C -TVMCalcs.com