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Annuity Calculator

Enter any four values and solve for the fifth — with amortization table and formula view

Click a variable badge to select the value to solve for

Rate per payment period

Enter a decimal value or fraction (e.g., 5/12)

Number of payment periods

Enter an integer value or calculate the number of periods (e.g., 12*30).

Coupon or annuity payment

Enter a positive value for cash inflows and a negative value for cash outflows

Present value or current price

Enter a positive value for cash inflows and a negative value for cash outflows

Future value or face value

Enter a positive value for cash inflows and a negative value for cash outflows

Amortization table Calculations NPV Profile

Period	Starting Balance	Interest	Payment	Ending Balance

Instructions

How to use: Enter any four of the five variables (RATE, NPER, PMT, PV, FV) and click the badge of the variable you want to solve for. The calculator will compute the missing value automatically.

Sign convention: Use positive values for cash inflows (money received) and negative values for cash outflows (money paid).

Input formats

RATE: Enter as a percentage (e.g., 8 for 8%). You can also use fractions like 5/12 for a monthly rate derived from 5% annual.
NPER: Enter the number of periods. You can use expressions like 12*30 for 360 monthly payments.
PMT, PV, FV: Enter numeric values. Use negative for outflows (e.g., -2000 for a $2,000 payment).

Display modes

Amortization table: Shows how the balance evolves each period with interest and payments.
Calculations: Displays the annuity equation (Eq. 4.13), the solution with your values substituted, and the equivalent Excel formula.
NPV Profile: (Custom Cash Flows mode only) Plots NPV against a range of discount rates. The IRR is where the curve crosses zero. The current discount rate (in NPV mode) is also marked on the chart.

Custom Cash Flows Mode

NPV: Enter a discount rate and individual cash flows for each period. Period 0 is typically the initial investment (negative).
IRR: Enter cash flows only. The calculator finds all rates that make NPV equal to zero. Cash flows must have at least one sign change.
Multiple IRRs: When cash flows change sign more than once (e.g., +550, −500, −500, −500, +1000), multiple IRRs may exist. All are displayed and marked on the NPV Profile chart.
No IRR: Some cash flow patterns have no IRR (NPV never crosses zero). The NPV Profile chart still shows the curve.
Excel equivalent: =NPV(rate, CF1:CFn) + CF0 for NPV, =IRR({CF0,CF1,...,CFn}) for IRR.

Annuity Equation (Eq. 4.13)

The equation states that the present value of all cash flows equals zero: the initial value (PV) plus the present value of all periodic payments (PMT) plus the present value of the future value (FV).