Annuity Calculator Solve for N

An annuity is a series of equal payments made at regular intervals. This calculator helps you determine the number of periods (n) in an annuity when you know the payment amount, interest rate, and present value or future value.

What is an Annuity?

An annuity is a financial product that provides a series of equal payments at regular intervals. There are two main types:

Ordinary Annuity: Payments are made at the end of each period.
Annuity Due: Payments are made at the beginning of each period.

Annuities are commonly used in retirement planning, mortgages, and insurance products. They provide a steady income stream over time.

Solving for Number of Periods (n)

When calculating the number of periods in an annuity, you typically know:

The payment amount (PMT)
The interest rate (r)
Either the present value (PV) or future value (FV)

The number of periods (n) is what you're solving for. This is useful when planning for retirement, calculating loan terms, or determining how long it will take to reach a financial goal.

Note: The interest rate should be the periodic rate (e.g., monthly rate for monthly payments).

Example Calculation

Let's say you want to know how many years it will take to save $100,000 if you invest $5,000 at the end of each year at a 5% annual interest rate.

Using the annuity formula:

FV = PMT × [(1 + r)ⁿ - 1] / r

Plugging in the numbers:

$100,000 = $5,000 × [(1 + 0.05)ⁿ - 1] / 0.05

Solving for n gives approximately 10.5 years.

Formula

The formula to calculate the number of periods (n) in an annuity depends on whether you're working with present value or future value:

Present Value Annuity

PV = PMT × [(1 - (1 + r)^-n) / r]

Solve for n:

n = log(1 - (PV × r / PMT)) / log(1 + r)

Future Value Annuity

FV = PMT × [(1 + r)ⁿ - 1] / r

Solve for n:

n = log(1 + (FV × r / PMT)) / log(1 + r)

Where:

PV = Present Value
FV = Future Value
PMT = Payment amount
r = Interest rate per period
n = Number of periods

FAQ

What's the difference between an ordinary annuity and an annuity due?

An ordinary annuity makes payments at the end of each period, while an annuity due makes payments at the beginning of each period. This affects the calculation of present and future values.

How do I determine the periodic interest rate?

Divide the annual interest rate by the number of periods per year. For example, a 6% annual rate with monthly payments would be 0.5% per month (6% ÷ 12).

Can I use this calculator for loans?

Yes, you can use this calculator to determine the number of payments needed to pay off a loan by entering the loan amount as the present value and the monthly payment as the payment amount.