How does compound interest work

What is compound interest?

Compound interest is interest you get on both the principal you initially deposit and the interest you’ve already earned. The longer the money is in the account (whether it’s a savings account or a loan), the more the total amount will be.

How to calculate compound interest

To calculate compound interest, use the below formula:

Total Amount with Compound Interest = P * (1 + r)ⁿ

• P is the principal amount (the initial sum of money)
• r is the interest rate per period (expressed as a decimal)
• n is the number of time periods

With a savings account, compound interest is a great thing. While the amount you’ve made from interest won’t be very high initially, the longer you keep your money in the account, the more compound interest you’ll accrue.

For example, a $10,000 contribution into an account with a five percent annual interest rate compounded monthly over five years would yield $12,833.59 or $2,833.59 in interest. Over several years, you can earn hundreds or even thousands of dollars in interest without ever having to adjust your principal contribution. 

Below is a comparison table illustrating how investments of $10,000 and $20,000 grow over time with a 5% annual interest rate compounded monthly. It highlights the increasing impact of compound interest over 1 to 20 years, showcasing substantial growth in your investment as time goes on.

How compound interest works for home mortgages

Compound interest works the other way, too. Though a savings account will increase the money you earn each month, many home mortgages use compound interest to determine what you’ll pay in interest each month.

For instance, if you’re buying a home, you may have a mortgage that compounds monthly. That means each month, the current outstanding interest will get added back to your principal. Other mortgages may compound weekly or daily.

Let's explore an example to illustrate how compound interest affects mortgage amounts over time. Imagine two mortgages, one for $300,000 and another for $500,000, both accruing interest at a 4% annual rate, compounded monthly. Below is a table showing how these mortgages grow over different time periods:

How to reduce your home mortgage interest

Unless you can pay in full in cash when you buy your house, you’ll encounter interest over the course of your mortgage. A real estate professional can walk you through what your monthly payments will look like, but there are a couple of ways to reduce the amount of interest you have to pay on a home mortgage.

1. Pay more than your monthly payment each month

Any money that goes beyond your monthly payment will be applied exclusively to your principal. For example, if your monthly payment is typically $2,000 (including principal and interest), you could set your monthly payment to be $2,100, with the additional $100 going toward paying off your principal. 

While this can be a good strategy, never spend outside of your means simply to pay a mortgage off more quickly. 

2. Set up a biweekly payment plan

A biweekly payment plan is just what it sounds like: you’ll pay off your mortgage every two weeks. Using the example above, a $2,000 monthly payment would be broken down into $1,000 payments every two weeks.

A typical mortgage has 12 payments per year — one for each month. With a biweekly payment plan, you’re actually making 26 payments split up over the year. In other words, you’re getting an extra month knocked off your principal every year.

Biweekly payments can be a quicker way to pay off your mortgage. You’re contributing an extra monthly payment every year that goes toward your principal. And because you’re making more payments, you’re reducing the amount of interest you’ll pay over the course of the loan. 

However, be careful when considering a switch to a biweekly payment. Make sure you can still afford a withdrawal twice a month (especially if you’re not paid on a regular schedule) and have a good sense of your finances before making the switch. Once you do, you can’t change back.

How compound interest works for life insurance

What is simple interest?

You may also come across simple interest, which is interest calculated on a loan’s principal or your initial contribution to a savings account. As the name suggests, simple interest doesn’t compound, so you’d only make money on your original payment or contribution.

How to calculate simple interest

To calculate simple interest, use the below formula:

Total Amount with Simple Interest = P * (1 + r * t)

• P is the principal, or initial, amount.
• R is the annual interest rate as a decimal
• T is the time duration in years.

For example, that same $10,000 contribution at a five percent annual interest rate over five years would yield $12,500 total, or an additional $2,500 from the simple interest.

Simple interest is less common than compound interest, though you still may find it in short-term loans or car loans. If you have a biweekly mortgage instead of a monthly payment, you may also encounter simple interest calculations.

How simple interest works for auto loans

If you’re deciding between buying a new or used car, you’ll likely finance it with an auto loan. A new car is often eligible for lower interest rates when financing with the dealer, so you’ll pay less interest over the life of the new car loan. A used car typically sees higher interest rates to make up for the lower principal cost.

In both situations, you’ll continue paying interest on the principal cost. Car loan interest is front-loaded, or amortized, so the majority of your early payments will go toward paying down the loan’s interest. As you keep making payments, more of that money will go toward paying off the principal. 

You can reduce your principal by making a down payment or trading in your current ride for a new one. You’ll also likely encounter other costs, from sales tax and registration fees to origination fees and extended warranties.

Here's a table that explains car interest rates and how much you'll pay over time, assuming a car loan amount of $20,000. The table varies the interest rates and loan terms to show different scenarios:

This table shows that longer loan terms and higher interest rates result in higher total interest paid, even though the monthly payments might be lower. Conversely, higher monthly payments over shorter terms lead to less total interest paid. Keep in mind that the exact figures can vary based on the specific terms of your loan and any additional fees or costs associated with the loan. ​

But what about APR?

While car shopping, you may also see the term APR, which stands for Annual Percentage Rate. It reflects the true cost of a car loan, encompassing not just the interest but other loan fees and additional costs like sales tax, service and extended warranties and Guaranteed Asset Protection.     

In almost every case, the APR will be higher than the interest rate, because it’s looking at a higher total cost. However, some car dealerships may offer special deals or incentives to lower the APR. Federal law mandates that APRs must be provided for car loans, so you can compare it with the interest rates to find what works best for you.

Interest can work both for and against you, but it’s important to understand how it works in every situation. With that knowledge, you could potentially earn — or save — a lot of money.

Other resources to check out

Interest can work both for and against you, but it’s important to understand how it works in every situation. With that knowledge, you could potentially earn — or save — a lot of money.

Check out these other resources to continue your personal fianance journey:

5 apps and websites to make money simply by living

15 ways a smart home office can boost productivity and wellness

Claims, deductions, and exemptions, Oh my! How working remotely can affect your taxes