Finance · 5 min read
How to Calculate Present Value and Annuity Payments
Discount a lump sum — or a stream of level payments — back to today
Present value asks what a future cash amount is worth now at a constant period rate. This tutorial walks through PV = FV(1 + r)^(−n) for a lump sum, the ordinary-annuity formula for level end-of-period payments, a $1,000 / 5% / 10-period worked example, and a playground that compares the two as you move r and n. Figures are illustrative; fees and taxes are omitted.
Written by the My Calculator Stack editorial team. About our methods
These figures are illustrative. Fees, taxes, and product-specific rules are omitted. This is not investment, tax, or financial advice.
1.What present value is
Present value is the amount you would set aside today so that, after it earns a constant rate for n periods, it matches a future cash flow. A lump sum is one future amount. An ordinary annuity is a stream of equal payments at the end of each period. The rate r is per period, matching n — if you have a 6% annual rate with monthly compounding, use 0.5% per period and count months. Fees and taxes are not in these formulas.
2.The formulas
A lump sum discounts with PV = FV / (1 + r)^n, or FV(1 + r)^(−n). r is the period rate as a decimal (5% → 0.05). An ordinary annuity of PMT per period is PV = PMT × [1 − (1 + r)^(−n)] / r. If r = 0, the annuity is simply PMT × n. These are end-of-period payments, not an annuity due (which pays at the start of each period). Present value is the inverse of the future-value growth on this site: FV = PV(1 + r)^n.
\[ \begin{aligned}\mathrm{PV}_{\mathrm{lump}} &= \mathrm{FV}\,(1 + r)^{-n} \\\mathrm{PV}_{\mathrm{annuity}} &= \mathrm{PMT}\,\frac{1-(1+r)^{-n}}{r}\end{aligned} \]
3.Worked example
Take a $1,000 future amount at 5% per period for 10 periods — the same defaults as the future value calculator, run in reverse. Then PV = 1000 / (1.05)^10 ≈ $613.91. An ordinary annuity of $100 per period at the same r and n is PV = 100 × [1 − (1.05)^(−10)] / 0.05 ≈ $772.17. Raising r or n cuts both present values; the annuity still stacks ten payments, so it stays larger than the single lump at these inputs.
\[ \mathrm{PV}=1000(1.05)^{-10}\approx 613.91 \]
4.Lump sum versus ordinary annuity
Move the period rate and the number of periods to see both present values update. The bars compare a single future amount with a stream of level end-of-period payments. This is a teaching widget — no fees, no annuity-due switch, no full calculator chrome. Open the future value calculator when you want the standalone compounding tool, or a loan calculator when the unknown is a payment that amortizes a present principal.
Inline playground
Illustrative — fees and taxes omitted
Present value
Lump $613.91 · annuity $772.17
1000 × (1.05)^(−10) ≈ 613.91
Illustrative only — constant period rate, end-of-period annuity payments, no fees or taxes.
Open the full future value calculator →5.Open the full calculator
The future value calculator uses the inverse equation FV = PV(1 + r)^n, the same $1,000 / 5% / 10-period example, and the same limitation that taxes and fees are omitted. Browse other finance tools if you need compound interest with a compounding frequency, a loan payment, or an amortization schedule next.
Try it yourself
Open the related calculator and put these formulas to work.