# Series 7

## Getting Started - Calculating Simple and Compound Interest

Here we are going to start simple and work our way up to the more complicated formulas often seen in Series 7 exam situations.

Simple Interest
Interest is the cost of borrowing money, or is the amount you receive from lending money. To calculate, you take the amount of the loan, known as the principal, and multiply it by the rate, which is the annual percentage being charged. Multiply the result by the time to maturity.

 Simple Interest = (Principal x Rate) x Time

For example, let's say you're borrowing \$100,000 at a 5% annual rate for three years. (Remember, 5% is the same as 0.05.) Multiply \$100,000 by 0.05 and the result is \$5,000. This means you will pay \$5,000 in interest if you hold on to that money for exactly one year. But now you must multiply that by 3, the number of years that you are borrowing the money. The final result is \$15,000 (\$5,000 x 3), and that is the amount of interest you would have to pay throughout the term of your loan.

However, this example assumes you are taking out the full \$100,000 as a lump sum and paying it back in one tidy payment exactly three years later. Reality is more complex than that, so you need to be familiar with the concept of compounding.

Compound Interest
Compound interest occurs in most instances, and is generated from the ability of reinvested earnings (or the remaining principal) to earn interest on interest.

Let's consider a similar example. Say you deposited \$100,000 in the bank at 5% annual interest. After a year, you would have \$105,000, but you cannot just tack on another 5% every year. For Year 2 you would have to calculate what 5% of \$105,000 is, and add that on, then for Year 3, figure out what 5% of the Year 2 figure is and add that to the mix.

Before looking at the equation used to calculate this, let's see how you proceed, conceptually, assuming the same three-year timeline:
2. Multiply it by 1 + the interest rate. In the example the interest rate is 5% so the factor is 1.05 and the result is \$105,000.
3. Multiply the Year 2 figure by 1 + the interest rate. In this example the result is \$110,250 (\$105,000 x 1.05).
4. Repeat Step 3 for all subsequent years. In this example there is only one more year, so the final result is \$115,762.50.
As the depositor in this example, you benefit from compound interest. With simple interest you would have earned only \$115,000; the other \$762.50 is interest on the interest.

Here is the equation:

 Future Value (FV) = PV x (1+r)n
Where:
• FV is future value (the total at the end of the period, for which you are solving)
• PV is the present value (the amount deposited today)
• r is the interest rate
• n is the number of periods for which r is compounded (years, in this simple example).
Following this formula will save you some steps:
1. Take 1 + the interest rate and raise it to the power of the number of years. In this example that would be 1.157625 (1.053).
2. Multiply by the initial deposit. The final result is \$115,762.50 (\$100,000 x 1.157625).
If you consider how complicated it would be to calculate the compounding on an investment with a 30-year time horizon, you see how much simpler it is to use the equation.