HOW MUCH WEALTH DO YOU NEED? THE ONLINE PERSONAL FINANCE TRACKER

The most basic method of calculating interest is the simple interest method. The other, more common method of calculating interest is the compound interest method (described in section 6).
Interest is the cost charged or payment made for the use of money. The simple interest method calculates interest on the principal only without any compounding. In other words, the interest earned is not used to earn further interest.
The elements used to determine simple interest are the principal, the rate of interest, and the length of time that the principal is invested or borrowed. The formula for simple interest is as follows:
Interest = Principal Amount × Annual Interest Rate × Time Period
or
I = P × R × T
For example, $2,000 deposited for two years at 5 percent per annum would earn $200 in simple interest ($2,000 × 2 × 0.05). The total amount received at the end of two years would be $2,200, the principal amount plus the interest.
WORKSHEET 5.1 How to calculate simple interest
Principal amount P
Annual interest rate R
Time period of deposit or loan T
Simple interest = P × R × T

The following example illustrates simple interest earned when the amount is deposited for less than a year. A principal amount of $2,000 is deposited in a certi.cate of deposit at an annual rate of 6 percent for six months. The interest is $60 ($2,000 × 0.06 × 6 ÷ 12).
The rate can be expressed in decimal form or as a fraction (0.06 or 6 ÷ 100, respectively). The time is shown in months (6 ÷ 12). It can also be expressed in days (360 per year, used by banks, or 365 days). Worksheet 5.1 provides the framework for you to calculate simple interest on a deposit or loan.

Compound Interest and How to Determine Future Value.
Compound interest differs from simple interest in that interest is paid not only on the principal but also on the accumulated interest, assuming that the interest is left to accumulate. The greater the number of periods for which interest is calculated, the greater the accumulation of interest earned on interest plus interest earned on the principal. The formula for compound interest is expressed as follows:
Future Value = Principal (1 + Interest Rate)n
FV = P (1 + i)n where
FV = Total future value (principal plus total compound interest)
P = Principal (amount invested)
i = Interest rate per year or annual percentage rate
n = The number of periods at the interest rate
To illustrate the difference between simple and compound interest, assume that $100 is invested at 5 percent per year for three years and the interest is not withdrawn. If compounded annually, the compound interest earned would be $15.76, while the simple interest earned would be $15, as shown in Figure 6.1.
The principal amount of $100 is used to determine the interest in the simple interest method, whereas compound interest uses the principal plus the accumulated interest from the previous year to calculate the interest for the next year. Thus, when given a choice between investing in a simple interest or compound interest account, you would choose compound interest, assuming risk and all other factors are the same.
FIGURE 6.1 Simple interest versus compound interest
Simple interest Compound interest
Year 1 $100 × 5%; FV = $105.00 $100.00 × 5% = $5.00; FV $105.00 Year 2 $100 × 5%; FV = $110.00 $105.00 × 5% = $5.25; FV $110.25 Year 3 $100 × 5%; FV = $115.00 $110.25 × 5% = $5.51; FV $115.76
Total interest = $15.00 Total interest = $15.76
FV = Future value.

The formula below includes modi.cations to take into account nonannual compounding periods:
FV = P(1 + i ÷ m)mn
where FV = Total future value at the end of n periods
P = Principal or original amount invested
I = Annual compound interest rate
m = The number of times compounding occurs during the year
n = The number of years of compounding
Using Financial Tables to Determine the Future Value

Future values can be determined by using the compound sum of $1.

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