Updated Finance & Retirement Tool

Annuities Calculator

Compute future value, present value and payments for ordinary annuities and annuity due. Plan savings, loans and retirement income with clear formulas and step-by-step outputs.

Future Value Of Annuity Present Value & Payments Retirement Savings Planner Withdrawal Income Annuity

Interactive Annuity Suite – FV, PV, Payments And Retirement

Use this Annuities Calculator to connect payment amount, interest rate, number of periods, present value and future value. Switch between tabs to model savings plans, level payment loans and retirement income.

Future value uses the periodic rate and total number of periods. The calculator adjusts the annual rate and years automatically based on payment frequency.

Present value discounts each payment back to today using the per-period interest rate and total number of periods.

Enter a future value goal, a present value or both. The calculator uses the appropriate annuity formulas to solve for the periodic payment amount.

The retirement planner treats your contributions as an annuity building up to a target future value at retirement.

Treat your balance as the present value of an annuity and solve for the regular payout amount over the chosen number of years.

The table summarizes total contributions and accumulated future value at the end of each year for the selected annuity type.

Use this tab to see how the core annuity formulas behave for a single example set of inputs.

Annuities Calculator – Future Value, Present Value And Payment Formulas

The Annuities Calculator on MyTimeCalculator connects all the core annuity variables in one place: payment per period, interest rate, number of periods, present value and future value. Instead of memorizing several different formulas, you can move between them with dedicated tabs for future value, present value, payment amount, retirement savings and withdrawal income.

Annuities appear everywhere in personal finance: monthly savings into an investment account, fixed payment loans, pension income streams and structured payouts. Once you understand the basic annuity formulas, these situations become much easier to compare and plan.

Time Value Of Money And Annuity Building Blocks

An annuity is a level stream of cash flows. The key ingredients are:

  • \( P \): the payment made each period
  • \( r \): the periodic interest rate
  • \( n \): the total number of periods
  • \( FV \): the future value at the end of the schedule
  • \( PV \): the present value today

The calculator converts your annual interest rate and payment frequency into per-period values using:

\( r = \dfrac{i}{m} \)
\( n = \text{years} \times m \)

Here \( i \) is the annual rate (in decimal) and \( m \) is the number of payments per year (12 for monthly, 4 for quarterly, 1 for yearly).

Future Value Of An Ordinary Annuity And Annuity Due

The future value of an ordinary annuity assumes payments happen at the end of each period. The formula is:

\( FV_{\text{ordinary}} = P \cdot \dfrac{(1+r)^n - 1}{r} \)

For an annuity due, payments happen at the beginning of each period, so each cash flow has one extra period to earn interest. The future value is:

\( FV_{\text{due}} = P \cdot \dfrac{(1+r)^n - 1}{r} \cdot (1+r) \)

The Future Value tab in the calculator computes both values, shows total contributions \( P \times n \) and separates the growth portion as \( FV - \text{contributions} \).

Present Value Of An Ordinary Annuity And Annuity Due

Present value discounts all future payments back to today. For an ordinary annuity, the formula is:

\( PV_{\text{ordinary}} = P \cdot \dfrac{1 - (1+r)^{-n}}{r} \)

For an annuity due, each payment is received one period earlier, so the present value is higher by a factor of \( 1+r \):

\( PV_{\text{due}} = P \cdot \dfrac{1 - (1+r)^{-n}}{r} \cdot (1+r) \)

The Present Value tab applies these formulas and compares the nominal total of payments \( P \times n \) with the discounted present value to show the impact of the interest rate.

Solving For The Required Payment

Often you know the value you want and need to solve for the periodic payment. Rearranging the ordinary annuity formulas gives two importantationships.

For a target future value \( FV \):

\( P = FV \cdot \dfrac{r}{(1+r)^n - 1} \)

For a target present value \( PV \) (such as a loan amount):

\( P = PV \cdot \dfrac{r}{1 - (1+r)^{-n}} \)

For annuity due versions, the calculator divides the ordinary annuity payment by \( 1+r \) because each payment is shifted one period earlier. On the Payment tab you can enter a future value, a present value or both and see the implied payments.

Retirement Savings As An Annuity

Regular retirement contributions are a classic example of an annuity building toward a future goal. If you want a target balance \( FV \), the ordinary annuity contribution needed is:

\( P = FV \cdot \dfrac{r}{(1+r)^n - 1} \)

The Retirement Planner tab uses this formula and also shows:

  • Total contributions \( P \times n \)
  • Estimated investment growth \( FV - P \times n \)
  • Alternative contribution if payments are treated as an annuity due

You can experiment with different rates, years and frequencies to see how compounding accelerates growth over long time horizons.

Withdrawal Annuity For Retirement Income

A payout annuity starts from a known present value and solves for a level withdrawal that will exhaust the balance over a chosen period. The payment for an ordinary payout annuity is:

\( P = PV \cdot \dfrac{r}{1 - (1+r)^{-n}} \)

The Withdrawal Annuity tab applies this formula, reports total withdrawals \( P \times n \) and separates the interest earned during the payout phase as:

\( \text{Payout Interest} = P \times n - PV \)

For an annuity due payout, withdrawals are assumed to happen at the beginning of each period, which increases the payment slightly compared to the ordinary case.

How The Annuity Table Is Built

The Annuity Table tab summarizes how contributions and future value build up over time. For each year \( k \) from 1 to the total number of years, the calculator computes:

\( n_k = k \times m \)
\( \text{Contrib}_k = P \times n_k \)
\( FV_k = P \cdot \dfrac{(1+r)^{n_k} - 1}{r} \) for an ordinary annuity

For an annuity due version, \( FV_k \) is multiplied by \( 1+r \). The table then reports growth as:

\( \text{Growth}_k = FV_k - \text{Contrib}_k \)

Worked Example: Future Value Of An Annuity

Suppose you invest 200 per month for 10 years at an annual rate of 6%, compounded monthly. The periodic rate and number of periods are:

\( r = \dfrac{0.06}{12} = 0.005 \)
\( n = 10 \times 12 = 120 \)

The future value of the ordinary annuity is:

\( FV_{\text{ordinary}} = 200 \cdot \dfrac{(1+0.005)^{120} - 1}{0.005} \)

The calculator evaluates this expression numerically, compares it with total contributions \( 200 \times 120 = 24{,}000 \) and shows how much of the final balance comes from growth.

How To Use The Annuities Calculator Step-By-Step

  • Choose the tab that matches your question: future value, present value, payment, retirement or withdrawal income.
  • Enter the known quantities such as payment, years, rate, target future value or present value.
  • Select payment frequency and annuity type (ordinary or due) to match the real timing of cash flows.
  • Click the calculate button to see key outputs along with totals, growth and comparisons.
  • Use the Annuity Table and Formula Explorer tabs to visualize growth and verify that the formulas behave as expected.

Interpreting Results And Practical Considerations

The formulas assume a constant interest rate, fixed payment schedule and no fees or taxes. Real-world products may include variable returns, charges, minimum guarantees or inflation adjustments. You can still use this calculator as a baseline, then layer on those additional details when comparing specific offerings.

For decisions pensions, life annuities or complex retirement strategies, it is a good idea to combine this tool with professional advice. The formulas make the time value of money transparent so that financial products are easier to understand and compare.

Annuities Calculator FAQs

Frequently Asked Questions Annuities

Learn how ordinary annuities, annuity due, present value and future value all connect in this calculator.

No. In mathematics and finance, an annuity simply means a level stream of payments. Many retirement products are structured as annuities, but savings plans, loans and leases are also modeled with the same formulas.

Use the Present Value or Payment tab. Enter the loan amount as present value, the annual interest rate, the term in years and the payment frequency. The calculator will show the required payment and theationship between total paid and the loan principal.

If payments are made at the end of each period, choose ordinary annuity. If payments occur at the beginning of each period, such as rent paid at the start of the month, choose annuity due. If you are unsure, you can select the option to show both and compare results.

The tool assumes a single consistent payment frequency for each calculation. For mixed schedules, you can break the problem into phases and run separate calculations, or approximate by converting everything to the most frequent payment interval.

The formulas contain powers of \( (1+r)^n \), so compounding amplifies differences in the rate as n grows. Over decades, even a one percentage point difference in annual return can lead to very different future values for the same contribution schedule.

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