Think & Done

Here we will have an in depth view of the way Present Value of Ordinary annuity and Annuity Due is calculated with mathematical formula and with MS Excel PV functions along with a handy calculator.
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Present Value Definition

As time passes money loses its face value, think of it this way, if someone borrowed $1000 from you today and returned the same amount in 10 years time, the money you will receive in ten years time will only be worth $632 if interest rates were to stay at 5% on average. Thus money depreciates as time goes by. This process of finding the worth of money receivable or payable at a future date is done with discounting the amount or stream of amounts at the discount rate.

Annuities with uneven cash flows

Usually we have annuities with constant stream of equal payment yet in good number of circumstances we are required to pay or deposit uneven amount of payments

Formula for Present Value of annuity with uneven cash flows

An Example to find Present Value of an annuity with uneven cash flows

Let us examine finding Present Value of annuity or PVA with an example investment proposal. Let us say we were offered a series of cash inflows at the end of each of the next four years as $5000, $4000, $3000, and $1000. And the discount rate is 12%.

PV at 12%

Annuities with constant cash flows

Most annuities require a series of periodic payment in same amount over a period of time. This is the most common type of annuity with constant cash flows.

Formula for Present Value of an annuity with constant cash flows?

Example of Present Value of an annuity with constant cash flows

Let us examine finding Present Value of annuity or PVA with an example investment proposal. Let us say we were offered a series of cash inflows at the end of each of the next four years in the amount of $1000. And the discount rate or return is 10%.

Present Value of an annuity @ 10%

User submitted Present Value of Annuities Questions/Problems

Debbie from Asked:

Present value of an annunity- What is the present value of the following annunities?
$3000 a year for 10 years discounted back to the present at 8%.
$50 a year for 3 years discounted back to the present at 3%.
$280 a year for 8 years discounted back to the present at 7%
$600 a year for 10 years discounted back to the present at 10%.

admin from Replied:

Hi Debbie

$3000 a year for 10 years discounted back to the present at 8%.
Ordinary Annuity ( End of period payments) : $20,130
Annuity Due: (Start of period payments): $21,741

$50 a year for 3 years discounted back to the present at 3%.
Ordinary Annuity ( End of period payments) : $141
Annuity Due: (Start of period payments): $146

$280 a year for 8 years discounted back to the present at 7%
Ordinary Annuity ( End of period payments) : $1,672
Annuity Due: (Start of period payments): $1,789

$600 a year for 10 years discounted back to the present at 10%.
Ordinary Annuity ( End of period payments) : $3,687
Annuity Due: (Start of period payments): $4,055

See the attached MS Excel Worksheet for Excel formulas to find present value of ordinary annuity and annuity due

	A	B	C	D	E
1	Present Value of Annuity
2	R	3000	50	280	600
3	N	10	3	8	10
4	I	8%	3%	7%	10%
5	PVA	=PV(B4,B3,B2,0,0)	=PV(C4,C3,C2,0,0)	=PV(D4,D3,D2,0,0)	=PV(E4,E3,E2,0,0)
6	PVAD	=PV(B4,B3,B2,0,1)	=PV(C4,C3,C2,0,1)	=PV(D4,D3,D2,0,1)	=PV(E4,E3,E2,0,1)
7