The present value of a 4-year ordinary annuity of $1000 per year starting in year 1 is the difference of 2 perpetuities.

Perpetuity 1 : $1000 per year starting in year 1
Perpetuity 2: $1000 per year starting in 5 years' time

Given a 5% discount rate, the present value of this annuity is ______.

Explanation: The first payment for Perpetuity 1 is at t = 1.
The first payment for Perpetuity 2 is at t = 5.

The formula for the present value of a perpetuity is PV = A/r, where A = annuity and r = rate. This formula is simple enough to use directly on your calculator.

For Perpetuity 1, PV at t = 0 is = 1000/0.05 = 20,000
For Perpetuity 2, we need to find the present value at t = 0. To do so, we need to first find the present value at t = 5-1 = 4, since an ordinary annuity has its first payment one period away. This also applies to a perpetual annuity. A = 1000, r at period 5 = 0.06. Thus, PV = 1000/0.05 = 20,000.
From the perspective of now (i.e., t = 0), the amount of 20,000 can be considered a future value. Thus, we now need to find the present value of this amount.

Using Texas Instruments BA II Plus:
Don't forget to clear your memories using 2nd QUIT and 2nd CLR WORK
20000 ± FV: FV = -20,000.00
4 N: N = 4.00
5 I/Y: I/Y = 5.00
CPT PV7: PV = 16,454.05

Using Hewlett Packard hp 12 C:
f CLEAR FIN: 0.00000000
f CLEAR REG: 0.00000000
4 n: 4.00000000
5 i: 5.00000000
20000 CHS FV: - 20,000.00000
g END: - 20,000.00000
PV: 16,454.04950

The present value of the 4-year annuity is x - PV(0) = 20,000 - 16,454.05 = 3,545.95.