## What Is an Interest Rate?

The interest rate is the amount a lender charges for the use of assets expressed as a percentage of the principal. The interest rate is typically noted on an annual basis known as the annual percentage rate (APR). The assets borrowed could include cash, consumer goods, or large assets such as a vehicle or building.

#### Interest Rates: Nominal and Real

### Key Takeaways

- The interest rate is the amount charged on top of the principal by a lender to a borrower for the use of assets.
- Most mortgages use simple interest. However, some loans use compound interest, which is applied to the principal but also to the accumulated interest of previous periods.
- A loan that is considered low risk by the lender will have a lower interest rate. A loan that is considered high risk will have a higher interest rate.
- Consumer loans typically use an APR, which does not use compound interest.
- The APY is the interest rate that is earned at a bank or credit union from a savings account or certificate of deposit (CD). Savings accounts and CDs use compounded interest.

## Understanding Interest Rates

Interest is essentially a rental or leasing charge to the borrower for the use of an asset. In the case of a large asset, such as a vehicle or building, the lease rate may serve as the interest rate. When the borrower is considered to be low risk by the lender, the borrower will usually be charged a lower interest rate. If the borrower is considered high risk, the interest rate that they are charged will be higher. Risk is typically assessed when a lender looks at a potential borrower's credit score, which is why it's important to have an excellent one if you want to qualify for the best loans.

For loans, the interest rate is applied to the principal, which is the amount of the loan. The interest rate is the cost of debt for the borrower and the rate of return for the lender.

## When Are Interest Rates Applied?

Interest rates apply to most lending or borrowing transactions. Individuals borrow money to purchase homes, fund projects, launch or fund businesses, or pay for college tuition. Businesses take loans to fund capital projects and expand their operations by purchasing fixed and long-term assets such as land, buildings, and machinery. Borrowed money is repaid either in a lump sum by a pre-determined date or in periodic installments.

The money to be repaid is usually more than the borrowed amount since lenders require compensation for the loss of use of the money during the loan period. The lender could have invested the funds during that period instead of providing a loan, which would have generated income from the asset. The difference between the total repayment sum and the original loan is the interest charged. The interest charged is applied to the principal amount.

For example, if an individual takes out a $300,000 mortgage from the bank and the loan agreement stipulates that the interest rate on the loan is 15%, this means that the borrower will have to pay the bank the original loan amount of $300,000 + (15% x $300,000) = $300,000 + $45,000 = $345,000.

If a company secures a $1.5 million loan from a lending institution that charges it 12%, the company must repay the principal $1.5 million + (12% x $1.5 million) = $1.5 million + $180,000 = $1.68 million.

### Simple Interest Rate

The examples above are calculated based on the annual simple interest formula, which is:

**$\textbf{Simple\ interest} = \text{principal}\times\text{interest rate}\times\text{time}$ **

The individual that took out a mortgage will have to pay $45,000 in interest at the end of the year, assuming it was only a one-year lending agreement. If the term of the loan was for 20 years, the interest payment will be:

**$\textbf{Simple\ interest} = \$300,000\times 15\%\times20=\$900,000$ **

An annual interest rate of 15% translates into an annual interest payment of $45,000. After 20 years, the lender would have made $45,000 x 20 years = $900,000 in interest payments, which explains how banks make their money.

## Compound Interest Rate

Some lenders prefer the compound interest method, which means that the borrower pays even more in interest. Compound interest also called interest on interest, is applied to the principal but also on the accumulated interest of previous periods. The bank assumes that at the end of the first year the borrower owes the principal plus interest for that year. The bank also assumes that at the end of the second year, the borrower owes the principal plus the interest for the first year plus the interest on interest for the first year.

The interest owed when compounding is higher than the interest owed using the simple interest method. The interest is charged monthly on the principal including accrued interest from the previous months. For shorter time frames, the calculation of interest will be similar for both methods. As the lending time increases, however, the disparity between the two types of interest calculations grows.

The table below is an illustration of how compound interest works.

Year | Beginning Loan | Interest 15% | Ending Loan |

1 | $300,000 | $45,000.00 | $345,000 |

2 | $345,000 | $51,750.00 | $396,750 |

3 | $396,000 | $59,512.50 | $456,263 |

4 | $456,263 | $68,439.68 | $524,702 |

5 | $524,702 | $78,705.28 | $603,407 |

6 | $603,407 | $90,511.07 | $693,918 |

7 | $693,918 | $104,087.73 | $798,006 |

8 | $798,006 | $119,700.89 | $917,707 |

9 | $917,707 | $137,656.03 | $1,055,363 |

10 | $1,055,363 | $158,304.43 | $1,213,667 |

11 | $1,213,667 | $182,050.10 | $1,395,717 |

12 | $1,395,717 | $209,357.61 | $1,605,075 |

13 | $1,605,075 | $240,761.25 | $1,845,836 |

14 | $1,845,836 | $276,875.44 | $2,122,712 |

15 | $2,122,712 | $318,406.76 | $2,441,118 |

16 | $2,441,118 | $366,167.77 | $2,807,286 |

17 | $2,807,286 | $421,092.94 | $3,228,379 |

18 | $3,228,379 | $484,256.88 | $3,712,636 |

19 | $3,712,636 | $556,895.41 | $4,269,531 |

20 | $4,269,531 | $640,429.72 | $4,909,961 |

At the end of 20 years, the total owed is almost $5 million on a $300,000 loan. A simpler method of calculating compound interest is to use the following formula:

$\begin{aligned}&\textbf{Compound interest}=\text{p}\times[(1+\text{interest rate)}^n-1]\\&\textbf{where:}\\&p=\text{principal}\\&n=\text{number of compounding periods}\end{aligned}$

When an entity saves money using a savings account, compound interest is favorable. The interest earned on these accounts is compounded and is compensation to the account holder for allowing the bank to use the deposited funds. If a business deposits $500,000 into a high-yield savings account, the bank can take $300,000 of these funds to use as a mortgage loan.

To compensate the business, the bank pays 6% interest into the account annually. So, while the bank is taking 15% from the borrower, it is giving 6% to the business account holder, or the bank's lender, netting it 9% in interest. In effect, savers lend the bank money, which, in turn, provides funds to borrowers in return for interest.

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## APR vs. APY

Interest rates on consumer loans are typically quoted as the annual percentage rate (APR). This is the rate of return that lenders demand for the ability to borrow their money. For example, the interest rate on credit cards is quoted as an APR. In our example above, 15% is the APR for the mortgagor or borrower. The APR does not consider compounded interest for the year.

The annual percentage yield (APY) is the interest rate that is earned at a bank or credit union from a savings account or certificate of deposit (CD). This interest rate takes compounding into account.

## Borrower's Cost of Debt

While interest rates represent interest income to the lender, they constitute a cost of debt to the borrower. Companies weigh the cost of borrowing against the cost of equity, such as dividend payments, to determine which source of funding will be the least expensive. Since most companies fund their capital by either taking on debt and/or issuing equity, the cost of the capital is evaluated to achieve an optimal capital structure.

## Interest Rate Drivers

The interest rate charged by banks is determined by a number of factors, such as the state of the economy. A country's central bank sets the interest rate, which each bank use to determine the APR range they offer. When the central bank sets interest rates at a high level, the cost of debt rises. When the cost of debt is high, it discourages people from borrowing and slows consumer demand. Also, interest rates tend to rise with inflation.

To combat inflation, banks may set higher reserve requirements, tight money supply ensues, or there is greater demand for credit. In a high-interest rate economy, people resort to saving their money since they receive more from the savings rate. The stock market suffers since investors would rather take advantage of the higher rate from savings than invest in the stock market with lower returns. Businesses also have limited access to capital funding through debt, which leads to economic contraction.

Economies are often stimulated during periods of low-interest rates because borrowers have access to loans at inexpensive rates. Since interest rates on savings are low, businesses and individuals are more likely to spend and purchase riskier investment vehicles such as stocks. This spending fuels the economy and provides an injection to capital markets leading to economic expansion. While governments prefer lower interest rates, a reason why the U.K. may never switch to the euro, they eventually lead to market disequilibrium where demand exceeds supply causing inflation. When inflation occurs, interest rates increase, which may relate to Walras' law.