Interest Rates

Interest rate formula and calculation

To find the interest rate using the formula, we need several pieces of information. Since the interest rate is the price of borrowing money, we need to know the amount of the original loan, which is also known as the principal amount, we need the amount that was paid back, and the time frame of the loan.

Formula and calculation

First, we figure out the amount of interest that is paid, then we can calculate the interest rate using the formula:

What if the loan does not have to be paid back in 1 year? What if the borrower has 5 years to pay back the loan? In that case, the interest rate is still calculated using the same formula, we just have to update the time period.

Setting the interest rate

We know how to calculate the interest rate on loans, but what dictates what an appropriate interest rate is?

The short answer: the supply and demand for money. The not-so-short answer: The Federal Open Market Committee sets a target federal funds rate, which is the average interest rate banks charge other banks on loans. This rate is determined by the federal funds market and affects the supply of money in the economy. The money supply can be influenced by the federal reserve via changes in the required reserve ratio, the discount rate, and open market operations.

Banks respond to these changes in requirements by adjusting the amount of lending by increasing or decreasing their interest rates. But, banks do not only take their own business needs into account when setting the interest rate. They also take into account the creditworthiness of the borrower. If the bank feels confident that the borrower will pay back the loan, then the interest rate will be lower since they are expecting to collect interest on all of the loan payments. However, if the bank feels that the borrower is at a higher default risk, it will set the interest rate higher to still be able to make money off of the payments even if the borrower does default.

Fig 1. - Equilibrium interest rate in the money market

To keep the economy stable, the Federal Reserve fixes the money supply at MS as seen in Figure 1 above, and wants to keep interest rates close to the equilibrium (E) where money supply (MS) is equal to money demand (MD). If the interest rate is too high at points H and r_H then the demand for money is less than the supply. To remedy this, banks lower interest rates to shift investment holding from savings to interest bearing assets. If interest rates are too low at L and r_L the demand for money exceeds the supply. Banks raise the interest rate to make borrowing more expensive, thereby encouraging people to save.

Examples of Interest rate

The most well-known example for people to come across interest rates is with their mortgage payment or their car loan. Most people do not have the entire purchase price of a house saved up. They go to a lender and ask for a loan to buy a house. The lender assesses the would-be homeowner's creditworthiness and provides them with the money to buy a house for a certain fee in the form of an interest rate. Often the interest rate is set, let's say at 3.5%, but sometimes the terms of the loan can stipulate an increase or decrease after a specified number of years. After 2 years the interest rate jumps to 6% or it can be floating and adjust with the market annually.

interest rates United States real interest rate studysmarter

Figure 2 shows the real interest rate in the United States from the year 1961 to 2020. The real interest rate is the interest rate after it has been adjusted for inflation. The nominal interest rate would be the actual interest rate of a year without taking into account the level of inflation.

Good interest rates

A good interest rate depends on which side of the transaction one is on. Every month, the borrower pays back a set portion of the loan. On top of that loan repayment, they also pay the interest. The bank eventually gets back the full amount of money it loaned out plus the money it made off of the interest payments. In this scenario, a high interest rate would benefit the bank but a low interest rate would benefit the borrower.

When interest rates are high, say at 6-10%, people may not want to borrow money but they will be encouraged to invest it. U.S. treasury bonds, certificates of deposit, corporate bonds, etc. pay interest to their holders. The interest payouts can come monthly, semi-annually, or annually depending on the bond. This allows an individual's savings to generate income and economic growth. If an individual is investing their savings into the market, a high interest rate is good because they earn more return.

Causes of an interest rate increase or decrease

Interest rates increase or decrease as a way of stabilizing the economy through monetary policy, government borrowing, the supply and demand of money, and inflation. The Federal Reserve intervenes in the market to implement its monetary objectives and control the money supply and inflation. Governments borrow to supplement their spending.

Interest rate increase

An increase in the interest rate can be caused by high inflation, an increase in the demand for money or credit, an increase in the supply of money, or increased government spending. When the money supply is high and there is high inflation, the Federal Reserve will implement monetary policy by increasing interest rates to pull money out of the market.

If the government increases its spending and has to borrow from the private sector via the loanable funds market, there is an increased demand for money. The increased demand for money drives interest rates up towards equilibrium with the money supply. This can cause private sector investment to be crowded out of the loanable funds market.

High interest rates can have a positive effect on the economy, because they help curb inflation when the economy is overheating and they earn lenders more interest on their savings. Inflation is reflected by the prices of goods. When inflation is smaller, the consumer's paycheck goes further in terms of how much they can buy. However, high interest rates may be okay in the short run, but in the long run, they discourage investment and lead to lower economic growth.

Interest rate decrease

A decrease in the interest rate can be seen when the government wants to increase the money supply and encourage borrowing. This can benefit the economy, because it encourages people to take out loans to invest in their businesses. This stimulates economic growth and development which leads to an increase in GDP. The downside to low interest rates is that consumers are discouraged from saving and inflation can increase due to the increased money supply in the market.