In today’s

economy,

inflation is inevitable. $10,000 today will not be worth $10,000 next year. Therefore, to keep the value of

money the same, one is forced to find ways to

invest his/her money to make more. One of the ways to do it is by

lending someone the money, and then

charging them interest. In the

United States, the safest way to do that is by depositing the money in a

bank. However, to make sure that one’s money are

earning as much as possible, one must first know all the different types of interest offered and what they mean. Interest is broken down into two categories,

simple interest and

compound interest.

**Simple Interest**

This is the interest that is earned only on the

initial amount. The

formula for calculating simple interest is:

SI = P

_{0}(

*i*)(

*n*)

Where SI = simple interest in

dollars
P

_{0} = principal, or original amount

borrowed (

lent) at time period 0

*i* =

interest rate per time period

*n* = number of time periods

To solve for the

future value (also known as the

terminal value) of the

account at the end of n years (FV

_{n}), the following formula is used:

PV

_{n} = P

_{0}(1 + (i)(n))

To calculate the present value (the current value of money)(P0) the following formula is used:

P

_{0} = FV

_{n}/(1 + (

*i*)(

*n*))

**Compound Interest**

This is the interest that is earned on the initial amount as well as any previous interest earned. This type of interest is most widely used. Because of its wide use, many forms of compound interest have been developed. The following are the most popular and widely used forms of compound interest.

**Single Amounts**

This compound interest is compounded every year. The formula used to find the future value of a compound interest is:

FV

_{n} = P

_{0}(1 +

*i*)

^{n}
To find the present value, the following formula is used:

P

_{0} = FV

_{n}(1/(1 +

*i*)

^{n})

**Annuities**

Annuities are series of equal payments or receipts (R) occurring over a specified number of periods (

*n*). Assuming that one will deposit every annuity at a fixed interest rate (

*i*) the following formula is used to find the future value of the annuity (FVA

_{n}):

R(((1 +

*i*)

^{n} – 1)/

*i*)

To find the present value of an annuity (PVA

_{n}) the following formula is used:

PVA

_{n} = R((1 – (1/(1 +

*i*)

^{n}))/

*i*)

**Compounding More Than Once a Year**

The general formula for solving for the future value at the end of n years where interest is paid m times a year is:

FV

_{n} = P

_{0}(1 + (

*i*/

*m*))

^{mn}
To find the present value of such compounding, the following formula is used:

P

_{0} = FV

_{n}/(1 + (

*i*/

*m*))

^{mn}
**Continuous Compounding**

In this compounding, the interest is compounded continuously. The general formula for such compounding, where interest is compounded continuously at a rate of i percent at the end of n years is:

FV

_{n} = P

_{0}(

*e*)

^{in}
The present value of this compounding is:

P

_{0} = FV

_{n}/(

*e*)

^{in}
These are the most common

types of compounding used in the banks of United States.