# Interest Types: Simple and Compound

Payment for the usage of money for a set period of time is called interest. Both a simple and a compound method exist for determining interest.

The amount of interest gained or lost is directly related to the distinction between the two.

## Regular Interest

Interest is said to be “simple” if it is calculated based solely on the principle amount for a given period of time.

That is, the interest rate will not change from period to period unless the principal amount of the note is modified.

The Compound Interest Formula for Simple Interest

When interest is calculated, both the original note amount and any accrued interest are factored in.

When compound interest is used, the interest accumulated for a given period is added to the principal sum from which interest is to be calculated in subsequent periods.

In this way, interest is earned or paid not only on the principal but also on the interest that is left on deposit through a process known as compounding.

## Example

Assume that the interest from the earlier example is now compounded annually rather than on a simple basis to illustrate the idea of compound interest.

Total interest income in this scenario is \$4,049.28, as shown in the table below, as opposed to the simpler case’s \$3,600.

Interest earnings in Year 1 total \$1,200 (12 percent of \$10,000). At the end of the year, the total amount owed would be \$11,200 because compound interest would have been added to the principal.

As a result, \$1,344.00 (or 12%) of \$11,200.00 is interest for the year, bringing the total amount accrued by the end of the second year to \$12,544.00.

At the end of year 3, the interest and total amount are calculated in the same manner.

How to Calculate Compound Interest and Amount

Below are the formulas for calculating the compound amount and compound interest.

Formula for a Composite Amount

How to Calculate Compound Interest

Compounded interest formula: Compound amount minus initial investment

## Example

A sole proprietor has received a loan from TD Bank in the amount of \$2,000 for a term of 5 years at an interest rate of 7%. Each year, the interest is added to the principal.

Required: Calculate the combined sum and interest at the compounded rate.

## Interest More Frequent Than Annual Compounding

The lender can determine how often interest is compounded. The rate at which interest accumulates is affected by how often it is compounded.

Many banks and credit unions, for instance, compute interest on a daily basis. This means that interest is added to your account daily based on the previous day’s opening balance.

The following day’s interest is calculated by adding this amount to the principal balance. Compared to yearly compounding, this is obviously more beneficial.

Adjustments for interest compounded at intervals other than once a year can be easily computed.

There would be multiple interest periods in a year if interest was compounded at intervals other than once per year.

If interest is compounded quarterly, for instance, each year would have four interest periods.

If interest were compounded weekly, our three-year investment would yield 12 interest periods.

However, the yearly interest rate should be adjusted downwards. Accordingly, the interest rate would be 3% per quarter rather than the 12% we used in our example.

The interest rate for each compounding period is calculated by dividing the yearly interest rate by the number of periods.

Interest compounded quarterly rather than annually results in a \$208.32 (from \$4,049.28 to \$4,257.60) rise in this simple example.