# Simple vs. Compound Interest: An Easy Guide

First Republic Bank
October 28, 2021

Interest is fundamental to the function of banking and finance. When you borrow money, you repay a predetermined amount on top of what you were loaned. The idea of interest is central to how people borrow and lend: when you’re the lender, you stand to earn interest on the money lent out, and when you borrow you expect the interest paid to be a fraction more of what you were lent.

As a borrower, it's important to look at the different types of interest you could be repaying back. Two of these types are simple interest and compound interest. Knowing the major differences between simple and compound interest is essential to maintaining your finances.

## Simple vs. compound interest

Simple interest is calculated once annually based on the principal balance only. So, after a year, a \$1,000 loan or investment with a 5% annual percentage rate (APR) would accrue \$50 in interest.

Compound interest is much more complex and varied. It’s charged on both the principal balance and any interest that has already accumulated. The compound interest rate is also often calculated more frequently (daily, monthly and quarterly).

Different financial information is relied on in the calculation of simple interest versus compound interest. Here’s how these two interest types differ:

 Simple Interest Compound Interest Charged on the principal yearly. That interest is then added to the principal balance Charge on both the principal and interest accrued Always calculated annually Calculated at various frequencies, including daily, monthly, quarterly or annually Interest rates can be fixed, depending on the institution Interest rates can be variable, depending on the account type

## How simple interest works

Simple interest lives up to its name; it’s a simple way to calculate interest using only the principal balance and excluding any interest that has already accrued annually. For example, simple interest on a \$30,000 auto loan with an annual interest rate of 2.25% over a 4 year time period comes out to \$2,700. To understand how that number is calculated, here’s the basic simple interest formula:​​

 Simple Interest Formula The formula for calculating simple interest is as follows: I = Prt I = interest accumulated P = initial principal balance r = interest rate t = number of time periods elapsed (in years)

Let's take a look at the example above again:

P = \$30,000 (auto loan)

r = .0225 (the interest rate 2.25% in decimal form)

t = 4 (time in years)

I = 30000*.0225*4

To find how much you’ll pay in interest, multiply the principal of \$30,000 by the interest rate (2.25%) and the number of time periods that have elapsed (4 years). This total comes out to \$2,700 — the amount of interest you’d pay on top of what you borrowed. That would mean that the full total you could expect to pay over 48 months would be \$32,700 (the principal and the accrued interest).

## How compound interest works

Compound interest can generate much higher totals than simple interest because of how (and what) the calculation includes. When you calculate compound interest, you’re basing your numbers on both the principal balance and any interest you’ve already accumulated.

This can make lending an expensive proposition: for example, if your credit card compounds interest daily, you’ll be paying the prior day’s interest on top of the existing principal balance, meaning your financial obligations will grow quickly.

On the other hand, compound interest can work for you. For example, if you invest in a retirement plan early and regularly, your initial investment benefits from compounding interest over time. If your investments compound interest over time, your future interest payments are calculated on your existing principal, as well as what you’ve already made via prior interest payments. The earlier you start saving, the longer period of time your investment has to grow.

So, for example, let's say you were to invest \$10,000 at an annual rate of return of 3.875%. Compounded interest would, over the span of one year, provide \$394.45, for a total amount of \$10,394.46. Here’s how to calculate that compound interest:

 Compound Interest Formula The formula for calculating compound interest is as follows:  A=P(1+r/n)nt A = final amount P = initial principal balance r = interest rate n = number of times interest applied per time period t = number of time periods elapsed (in months or years)

Let's apply this formula to the example above, 3.875% interest, compounding monthly on a \$10,000 balance:

P = 10000 (deposit amount)

r = .03875 (the 3.875% interest rate in decimal form)

n = 12 (months within the time period)

t = 1 (time period elapsed— in years)

Plugging the above information into the formula gives us:

A = 10,000.00(1 + 0.03875/12)(12)(1)

The parentheses go first.

A = 10,000.00(1.003229167)12

Then, the exponents and multiplication go second and third, leaving the account owner with:

A = \$10,394.46

So, investing \$10,000 at an annual rate of return of 3.875%. Compounded monthly over the span of one year would provide \$394.46, for a total amount of \$10,394.46.

This subtle difference can account for a significant difference in the amount of money you make—or owe—in interest.

## Simple vs. compound interest in practice

The kind of interest you might experience as part of a loan or investment may vary depending on the product. Installment loans, like auto loans and mortgages, use simple interest. This means you’ll end up paying less interest as your balance lowers.

Savings accounts and credit cards typically use compounding interest. That means you’ll accrue more interest as the life of the loan continues. This can be a good thing in the case of savings accounts but less so for credit card or student loan debt; the less you pay off on your original loan balance, the more the total amount (principal plus interest) owed accumulates because of interest.

Say, for example, that you have a \$5,000 loan with an APR of 15.16%. For this example, we’ll keep the APR steady.

 Principal APR Total Principal and Interest Balance, 1 yr. (simple) Total Principal and Interest Balance, 5 yr. (simple) Total Principal and Interest Balance, 1 yr. (compound, monthly) Total Principal and Interest Balance, 5 yr. (compound, monthly) \$5,000 15.16% \$5,758.00 \$8,790.00 \$5,812.00 \$10,619.48

The difference between simple and compound interest becomes stark when you look more closely at how compounding affects interest payments. That’s why considering the right lending option for you, as well as how your investments generate interest over time, is crucial. A financial partner like First Republic Bank can help you understand your options and determine what path might make the most sense for your needs and finances. You can learn more about our loans here. This information is governed by our Terms and Conditions of Use.