Annuity Calculator Find 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, present value, and future value.

What is an annuity?

An annuity is a financial product that provides a stream of fixed payments at regular intervals. It's commonly used in retirement planning, insurance, and savings strategies. 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 often used to calculate the future value of savings or the present value of a series of future payments.

How to find n in an annuity

Finding the number of periods (n) in an annuity requires knowing at least three of the following four variables:

Payment amount (PMT)
Interest rate (r)
Present value (PV)
Future value (FV)

You can use the annuity formula to solve for n when you have three of these values. The calculator on this page makes this calculation easy.

Formula for finding n

The formula to find the number of periods in an annuity is:

n = log(FV - PMT + (PV * (1 + r))) - log(PMT) ---------------------------- log(1 + r)

Where:

n = number of periods
FV = future value
PMT = payment amount
PV = present value
r = interest rate per period

Note: This formula assumes an ordinary annuity (payments at the end of each period). For an annuity due, the formula is slightly different.

Worked example

Let's calculate the number of periods for an annuity with:

Payment amount (PMT) = $1,000
Interest rate (r) = 5% (0.05)
Present value (PV) = $5,000
Future value (FV) = $0

Using the formula:

n = log(0 - 1000 + (5000 * 1.05)) - log(1000) ---------------------------- log(1.05)

Calculating step by step:

Inside the first log: 0 - 1000 + (5000 * 1.05) = -1000 + 5250 = 4250
First log: log(4250) ≈ 3.628
Second log: log(1000) ≈ 3.000
Numerator: 3.628 - 3.000 = 0.628
Denominator: log(1.05) ≈ 0.0212
Final calculation: 0.628 / 0.0212 ≈ 29.62

The result is approximately 29.62 periods. Since we can't have a fraction of a period in this context, we would typically round to 30 periods.

FAQ

What is the difference between an ordinary annuity and an annuity due?

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

Can I use this calculator for monthly payments?

Yes, you can use this calculator for any regular payment interval. Just make sure to enter the interest rate per period (e.g., monthly rate if payments are monthly).

What if I don't know the future value?

If you don't know the future value, you can set it to 0 in the calculator. This is common when calculating how long it will take to pay off a loan or reach a savings goal.