Chartered Financial Analyst and expert in debt valuation and time value of money concepts.
The **Present Value of Ordinary Annuity Calculator** determines the lump-sum amount today (Present Value) that is equivalent to a series of equal payments made at the end of each period (Ordinary Annuity). Enter any three of the core parameters (PV, PMT, Rate, or Term) to solve for the missing one.
Present Value of Ordinary Annuity Calculator
Instructions: Enter values for exactly three of the four core parameters to solve for the missing one.
Annuity Parameters
PVOA Formula
The core relationship for Present Value of an Ordinary Annuity (payment at end of period):
$$PV = PMT \left[ \frac{1 – (1 + R)^{-N}}{R} \right]$$ Formula Source: InvestopediaVariables Explained (Q, F, P, V – Parameters)
- $\text{PMT}$ (Periodic Payment, $Q$): The constant, recurring payment amount.
- $\text{PV}$ (Present Value, $F$): The lump-sum value of the annuity today.
- $R$ (Rate per Period, $P$): The interest rate per compounding period (e.g., annual rate / 12 for monthly).
- $N$ (Number of Periods, $V$): The total number of payments (e.g., years $\times$ 12 for monthly payments).
Related Annuity Calculators
Explore other time value of money concepts:
- Present Value of Annuity Due Calculator
- Future Value of Annuity Calculator
- Loan Principal Calculator
- Discount Rate Calculator
What is Present Value of Ordinary Annuity?
The **Present Value of an Ordinary Annuity** (PVOA) is the current value of a stream of equal payments received or paid at the end of each period for a specified time frame. The term “ordinary” specifically denotes that the cash flows occur at the end of the period, which is the convention for most loan payments and interest calculations.
PVOA is used widely in finance to determine the principal amount of a loan (since the principal is the present value of all future loan payments), to value pensions, or to calculate the lump sum required today to fund a future series of payouts.
How to Calculate PVOA (Example)
An investor is due to receive \$500 at the end of each year for 5 years. The discount rate is 8% per year (0.08). We want to find the present value ($\text{PV}$).
- Step 1: Determine the Annuity Factor
Calculate the discount factor for $N=5$ and $R=0.08$: $$\frac{1 – (1 + 0.08)^{-5}}{0.08} \approx \mathbf{3.9927}$$
- Step 2: Apply the Formula
$$PV = PMT \times \text{Annuity Factor}$$
- Step 3: Calculate the Result
$$PV = \$500 \times 3.9927 \approx \mathbf{\$1,996.35}$$
The present value of this annuity is $\mathbf{\$1,996.35}$.
Frequently Asked Questions (FAQ)
An Ordinary Annuity assumes payments are made at the **end** of the period (like a mortgage payment). An Annuity Due assumes payments are made at the **beginning** of the period (like rent). Annuity Due always results in a higher Present Value because the payments accrue interest for one additional period.
When you take out a loan, the loan’s principal amount is the Present Value of all your required future monthly payments (the Annuity). This is why the formula is central to amortization.
No. You must convert the annual rate to a rate per period. For monthly payments, divide the annual rate by 12, and use the total number of months (years $\times$ 12) for the number of periods ($N$).
If $R=0$, the formula simplifies to $PV = PMT \times N$, as no discounting is required. All future payments are equal to their present value.