The simple interest calculation only requires three inputs, which are the principal (or present value of the amount lent), the interest rate, and the number of time periods over which the principal is lent. Simply multiply the principal by the interest rate to get the amount of interest earned in one time period, and multiply that interest by the number of time periods over which the investment will grow in order to calculate how much interest the lender will earn in total. Generally, the time periods are years, but the periods can be days or weeks or any time period for that matter, as long as the rate is the rate given for the matching time period. The formula is shown below:
Where:
- I = Total interest earned
- P = Principal
- r = interest rate expressed as a decimal
- t = number of time periods
To calculate the future value with simple interest, we need the same three values in our calculation— the principal, an interest rate, and the number of time periods over which the money is lent. The formula is shown below:
Where:
- FV = Future Value
- P = Principal
- r = interest rate expressed as a decimal
- t = number of time periods
The future value with simple interest is the value of an amount today at some point in time in the future, where the interest paid is not compounded. This means that you do not re-lend or reinvest the interest. With just three values, we can see what an amount invested today will be worth in the future.
Example
Let’s walk through an example in order to understand how these formulas work. Say you lend $1,000 to a friend who promises to pay a 4% annual return, and he promises to give you the principal back in five years. The $1,000 is our principal, 4% is our interest rate, and five is t in terms of years. Notice that the rate is an annual rate, and our time periods are in years; hence, they match. After one year, your friend gives you $40 ($1,000 * 4%) as interest for letting him borrow your $1,000. Each year, your friend will pay you another $40 because you let him borrow your money, so each time period you earn another $40. This is the reason why we multiply the interest rate by the number of time periods. The following chart illustrates how this works.
| Year | Principal | Interest | Total |
|---|---|---|---|
| 1 | $1000 | $40 | $1040 |
| 2 | $1000 | $40 | $1080 |
| 3 | $1000 | $40 | $1120 |
| 4 | $1000 | $40 | $1160 |
| 5 | $1000 | $40 | $1200 |
To calculate your total interest earned, you just have to multiply your interest earned each year by the number of years. Interest earned each year is $40, and you are lending your money for five years, so over the course of those five years, you will earn $200 in interest ($40 * 5).
The future value after each year is your initial principal plus your accumulated interest, so your future value after five years is $1,200. You can also reach this number by plugging the values directly into the future value formula above like so:
