# How to calculate the present value of an annuity

## Ordinary pension and pension maturity

An annuity can be viewed as a way of making equal payments for a period of time, and it can be divided into two types: ordinary annuities and due annuities. According to the regular pension, periodic payments are made at the end of the period. Interest payments on bond issues are a good example of a decent pension. Another example that can be used is the present value of the cash flows from an investment. Both payments are usually made at the end of a period.

When the pension is due, regular payments are to be made at the beginning of the period. The leasing rates of business organizations are a very good example. When a company purchases property, plant and equipment (equipment, buildings), the leasing installments must be paid on the first day of the month. ie pension due.

## What is the present value of a pension?

The addition of the periodic payments discounted at a certain interest rate can be called the present value of an annuity. It is based on the concept of the time value of money, which means that the value of money will drop over time due to inflation, exchange rate fluctuations, etc. Hence, the value of cash is currently higher than it will be in future periods.

## Formulas for calculating the present value of an annuity

The following formulas can be used to calculate the present value of an annuity, which consists of the present value of the regular annuity and the present value of the annuity due. Where,

i = interest rate per compounding period = number of compounding periods R = fixed periodic payment

For example, when calculating the present value on 1/1/2013 of the annuity paid at the end of each month of 2013 of USD 1,000 at an interest rate of 15%, the calculation can be represented as follows:

R = 1000 n = 12 i = 15% / 12 = 1.25% Another example is that a certain amount was invested on 1/1/2013 that brings in \$ 2,000 at the beginning of each month in 2013. The interest rate on the investment was 18%. The initial investment and the interest earned can be calculated as follows:

R = 2.00n \$ = 12i = 18% / 12 = 1.5%

Original investment = PV of the annuity due on 01/01/2013 Amount of Interest Earned = [(\$ 2,000 * 12) - \$ 22,142.24] = \$ 1,857.76

Depending on the nature of the situation, the most closely related formula must be used to calculate the present value of an annuity. 