3.2 Interest
Two services typically offered by banks are savings accounts and loans. If you deposit money into a savings account, the amount of money in the account gradually increases. At a later date, you can withdraw more money than you deposited. In contrast, when you borrow money in the form of a loan, the total amount you will have to repay will be more than the amount you originally borrowed. In both of these scenarios, an increase in the amount of money is due to interest.
Interest is the cost of borrowing money. It is the amount of money that is paid in addition to the amount borrowed, loaned or invested. The original amount borrowed, loaned or invested is called the principal. Interest is charged on the principal due to the following factors:
- Inflation. As noted in the section 3.1, due to inflation money’s purchasing power slowly decreases. Without charging interest, the lender would be left with less purchasing power than they started with.
- Risk. There is a chance that the borrower will default on (not pay back) their loan. To account for this risk, lenders charge interest. The interest they earn helps cover losses from borrowers who are unable to make their payments.
An interest rate is a percentage rate applied on the principal, which is used to calculate the amount of interest generated in an interest period (the frequency that interest is calculated, e.g. monthly, bi-weekly, yearly).
There are two types of interest: simple interest and compound interest.
3.2.1 Simple Interest
Simple interest is calculated on the amount that was originally borrowed, loaned or invested – the principal. Interest accumulated in previous periods does not earn additional interest.
Example 3.1
Suppose you make a deposit of $100 in a bank account that pays 5% interest per year. After one year, you earn 5% interest, or $5, bringing your total balance to $105. After one more year, since simple interest is paid only on your principal, you again earn 5% of the original $100. That means you earn another $5 in the second year, and will earn $5 for every year of the investment. (Boundless Finance, 2016). The diagram below shows the interest the $100 deposit earns each year and how that affects the total value of your deposit. The next table shows account balances for this scenario for the first 5 years.
| Year | Beginning Balance | Interest Earned | Ending Balance |
| 0 | – | – | $100.00 |
| 1 | $100.00 | $5.00 | $105.00 |
| 2 | $105.00 | $5.00 | $110.00 |
| 3 | $110.00 | $5.00 | $115.00 |
| 4 | $115.00 | $5.00 | $120.00 |
| 5 | $120.00 | $5.00 | $125.00 |
Table 3.1 Simple Interest Earned on a $100 Deposit
Typically, the current account balance is called the present value ($100 in period 0) and the account balance at some point in the future is termed the future value ($125 in period 5).
The future value consists of the present value (principal) and the total interest:
(3.3)
Where F = Future Value
P = Present Value
I =Total Interest
Total interest I is the t