## Understand

An annuity is mean to secure steady cash inflows in future for individuals after their retirement years. For this, financial institutions make the contract and accumulate funds by getting equal cash installments from annuity holders. The phase in which funds are being accumulated is called accumulation phase, after a specific period, steady payments are made by the institution then the contract is in the annuitization stage.

In short, It is a series of equal installments, paid or received during a specific period of time. Annuity due and ordinary annuity are two types of annuities based on the duration of time when payment is made at the end of each period is called Ordinary annuity, and when payment is made at the start of each period is called Annuity due.

## Formula

The formula can be used for amortized loans, income annuities and other types of constant payment for a specific period of time.

For ordinary annuity, following formulas will be used,

Future value = P[(1+r)^{n}-1/r]

Present value = P[1-(1+r)^{-n}/r]

Where,

**P **is payment or equal installments to be paid.

**n **is a number of periods, which reflects how often payment is made for example if payment is made per month then the monthly rate will be used.

**r** is interest rate per period.

## How to calculate (Example)

**Example 1(Ordinary Annuity)**: You need to have $100,000 at the end of 5 years. For this, you decide to deposit a certain amount in a bank with 8% interest rate compounded annually. How much will you have to pay for the accumulation of $100,000 at the end of 5 years?

Solution:

We have,

Future Value (FV) = $100,000

Number of period (n) = 5 year

Interest rate (r) = 8%

Future value = P[(1+r)^{n}-1/r]

$100,000 = P[(1+0.08)^{5}-1/0.08]

P = $17,046