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Present Value of an Annuity Calculator

Find what a series of equal periodic payments is worth today, for payments at the end of each period or at the start.

What this tool does

Find what a series of equal periodic payments is worth today, for payments at the end of each period or at the start. You fill in these fields: Payment each period, Annual interest rate, Years, Payments per year, and Payment timing. It shows present value of the payments, total payments, interest component, and number of payments.

Inputs

  • Payment each period (USD): A number. Must be at least 0. The amount paid in each period.
  • Annual interest rate (%): A number. Accepts 0 to 100. The yearly discount rate. With more than one payment a year, the tool divides it by the number of payments per year.
  • Years: A number. Accepts 0 to 200. How long the payments last.
  • Payments per year: A whole number. Accepts 1 to 365. For example 1 for yearly, 4 for quarterly, 12 for monthly.
  • Payment timing: Choose one: End of each period (ordinary annuity), Start of each period (annuity due). Starts as End of each period (ordinary annuity).

How to use

  1. Enter the payment each period in USD.
  2. Enter the annual interest rate as a percentage.
  3. Enter the years.
  4. Enter the payments per year.
  5. Choose End of each period (ordinary annuity) or Start of each period (annuity due) for "Payment timing".
  6. Read the result: present value of the payments, total payments, interest component, and number of payments. It appears once every required field has a valid value.

Worked examples

Example 1. Inputs:

  • Payment each period: 1,000 USD
  • Annual interest rate: 5%
  • Years: 20
  • Payments per year: 1
  • Payment timing: End of each period (ordinary annuity)

Results:

  • Present value of the payments: $12,462.21
  • Total payments: $20,000.00 (Before discounting)
  • Interest component: $7,537.79 (Total payments minus present value)
  • Number of payments: 20

How this is worked out: Ordinary annuity: PV = P x (1 - (1 + r)^-n) / r with r = 0.05, n = 20. 1.05^20 = 2.6532977, its reciprocal 1.05^-20 = 0.3768895, so 1 - 0.3768895 = 0.6231105, divided by 0.05 = 12.462210. PV = 1000 x 12.462210 = 12462.21. Total payments = 1000 x 20 = 20000.

Example 2. Inputs:

  • Payment each period: 1,000 USD
  • Annual interest rate: 5%
  • Years: 20
  • Payments per year: 1
  • Payment timing: Start of each period (annuity due)

Results:

  • Present value of the payments: $13,085.32
  • Total payments: $20,000.00 (Before discounting)
  • Interest component: $6,914.68 (Total payments minus present value)
  • Number of payments: 20

How this is worked out: Annuity due: the ordinary annuity factor times (1 + r). 12.462210 x 1.05 = 13.085321. PV = 1000 x 13.085321 = 13085.32 (13085.3209 to four decimals). Total payments = 20000.

Example 3. Inputs:

  • Payment each period: 500 USD
  • Annual interest rate: 0%
  • Years: 10
  • Payments per year: 4
  • Payment timing: End of each period (ordinary annuity)

Results:

  • Present value of the payments: $20,000.00
  • Total payments: $20,000.00 (Before discounting)
  • Interest component: $0.00 (Total payments minus present value)
  • Number of payments: 40

How this is worked out: Zero rate: the present value equals the undiscounted total. Periods = 10 years x 4 per year = 40. Total = 500 x 40 = 20000, and PV = 20000 because nothing is discounted.

Example 4. Inputs:

  • Payment each period: 500 USD
  • Annual interest rate: 4%
  • Years: 10
  • Payments per year: 4
  • Payment timing: End of each period (ordinary annuity)

Results:

  • Present value of the payments: $16,417.34
  • Total payments: $20,000.00 (Before discounting)
  • Interest component: $3,582.66 (Total payments minus present value)
  • Number of payments: 40

How this is worked out: Quarterly payments: r = 4% / 4 = 0.01 per period, n = 10 x 4 = 40. 1.01^40 = 1.4888637 (seven figures), reciprocal 0.6716531, so 1 - 0.6716531 = 0.3283469, divided by 0.01 = 32.83469. PV = 500 x 32.83469 = 16417.345, which is accurate to about 0.01 at this working precision. Total = 500 x 40 = 20000.

Limitations

  • Assumes the same payment and the same rate for every period.
  • Assumes every payment is made on time and in full.
  • Years times payments per year should come to a whole number of payments. A part payment at the end is treated as a fraction of a period.
  • Shows the result in the currency you enter. It does not convert currencies.

FAQs

Q: What is the difference between an ordinary annuity and an annuity due?
A: An ordinary annuity pays at the end of each period. An annuity due pays at the start, which raises the present value by one period of interest. Choose Start of each period for an annuity due.
Q: What rate should I enter?
A: Enter the yearly rate as a percent. When you make payments more than once a year, the tool divides the yearly rate by the number of payments per year, so 4 percent paid quarterly uses 1 percent for each payment.
Q: How is the number of payments worked out?
A: It is the years multiplied by the payments per year. Ten years paid quarterly gives 40 payments.
Q: Does the result include taxes or inflation?
A: No. The payments are discounted at the rate you enter. Taxes, fees and inflation are not included.

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