# JAIIB AFB Unit 1 Calculation of Interest (Part 2)

## Present Value

Present value describes how much a future sum of money is worth today. Three most influential components of present value are : time, expected rate of return, and the size of the future cash flow. The concept of present value is one of the most fundamental and pervasive in the world of finance. It is the basis for stock pricing, bond pricing, financial modeling, banking, insurance, pension fund valuation. It accounts for the fact that money we receive today can be invested today to earn a return. In other words, present value accounts for the time value of money.

The formula for present value is:

PV = CF/(1+r)n

Where:
CF = cash flow in future period
r = the periodic rate of return or interest (also called the discount rate or the required rate of return)
n = number of periods

## Example :

Assume that you would like to put money in an account today to make sure your child has enough money in 10 years to buy a car. If you would like to give your child 10,00,000 in 10 years, and you know you can get 5% interest per year from a savings account during that time, how much should you put in the account now?

PV = 10,00,000/ (1 + .05)10 = 6,13,913/-

Thus, 6,13,913 will be worth 10,00,000 in 10 years if you can earn 5% each year. In other words, the present value of 10,00,000 in this scenario is 6,13,913.

## Future Value

The value of an asset or cash at a specified date in the future that is equivalent in value to a specified sum today. It refers to a method of calculating how much the present value (PV) of an asset or cash will be worth at a specific time in the future. There are two ways to calculate FV:

1) For an asset with simple annual interest: = Original Investment x (1+(interest rate*number of years))

2) For an asset with interest compounded annually: = Original Investment x ((1+interest rate)^number of years)

## Example

1) 10,000 invested for 5 years with simple annual interest of 10% would have a future value of

FV = 10000(1+(0.10*5))
= 10000(1+0.50)
= 10000*1.5
= 15000
2) 10,000 invested for 5 years at 10%, compounded annually has a future value of :

FV = 10000(1+0.10)5)
= 10000(1.10)5
= 10000*1.61051
= 16105.10

## Annuities

Annuities are essentially a series of fixed payments required from you or paid to you at a specified frequency over the course of a fixed time period. The most common payment frequencies are yearly, semi-annually (twice a year), quarterly and monthly. There are two basic types of annuities: ordinary annuities and annuities due.

Ordinary Annuity: Payments are required at the end of each period. For example, straight bonds usually pay coupon payments at the end of every six months until the bond's maturity date.

Annuity Due: Payments are required at the beginning of each period. Rent is an example of annuity due. You are usually required to pay rent when you first move in at the beginning of the month, and then on the first of each month thereafter.