### Understanding Annuities

An annuity is a method of accumulating a lump sum of money through a series of regular and equal payments and the reverse, being the liquidation of a lump sum through a series of regular and equal payments.

To annuitize a sum of money means to convert the sum to a series of monthly incomes such as the creation of a monthly retirement income flow.

To understand the math involved in the calculation, one should understand the basics of simple and compound interest. The process involves the interaction of value and time and the interest rate.

Example: ( Ordinary Annuity Certain)

What is the value of a monthly contribution of $100 over 5 years at an interest rate of 5%? compounding monthly.

Using a simple interest formula, one could go through the process of calculating the value of each contribution. Shown below, however, this would be a lot of work and can be calculated using a formula because the contribution amount and the intervals are consistent. See step 2 next for the actual annuity formula.

### Using the Annuity Formula - See Image Below

PMT = 100

N = 5yrs times 12 mos = 60

I = .05/12 = .004167

FV = 100(1.004167)60 -1 ÷ .004167

= 6,800.68.

2. Lump sum converted to an annuity payout.

Consider the situation where you have a lump sum of money that is to be payed out as an series of equal payments over time. Although the lump sum decreases in value, it still earns income on the unapportioned balance. This type of annuity is favored as a method of creating a monthly retirement income.

**Example:** John has accumulated 400,000 and would like to know how much that would pay him each month for the next 30 years. Interest rates are 5%.