Simple Interest and Principal Calculator
The simple interest calculator helps you figure out how much interest you’ll earn or owe over the course of a loan.
This tool is especially useful when analyzing different loan types to estimate the potential interest earned from lending money.
You can use this calculator to determine the principal, interest rate, or loan term.
Information Needed to Use the Simple Interest Calculator
To calculate simple interest, you’ll need several inputs. First, the principal loan amount. Then, you’ll need to either know or estimate the interest rate and loan term. The formula used is A = P(1 + rt), which includes:
- A: the total interest,
- P: the principal amount,
- r: the interest rate (in decimal form),
- t: the loan term.
You’ll need three of the four variables, so if you know A, P, and r, you can solve for t.
Understanding Simple Interest
Simple interest is the cost paid by a borrower to use borrowed funds for a specified period. It is calculated only on the original principal amount, meaning no interest is charged on previously accrued interest.
The simple interest rate remains constant over time, ensuring you always know how much you’ll pay.
Borrowers benefit from simple interest as they only pay interest on the principal. However, investors might find simple interest less profitable, as returns are lower compared to compound interest.
When repaying a simple interest loan, the first portion of each payment covers that month’s interest, while the remaining amount reduces the principal.
For instance, if you have a credit card with a 5% annual percentage rate and make $2,000 in purchases, you’ll owe the $2,000 principal plus 5% interest, resulting in a total repayment of $2,100.
Differences Between Simple and Compound Interest
Simple interest is calculated only on the principal balance, while compound interest takes into account both the principal and any previously accrued interest. As a result, compound interest grows faster than simple interest.
Compound interest is sometimes referred to as “interest on interest,” and its growth depends on how frequently it is compounded. The more compounding periods there are, the higher the interest.
The key difference between simple and compound interest lies in the growth rate: compound interest accumulates much faster.
Applications of Simple Interest
Simple interest applies to credit card balances, personal loans, student loans, mortgages, and most consumer loans, such as auto loans. Some certificates of deposit (CDs) also use simple interest to calculate returns.
Simple interest is commonly applied to short-term loans and some mortgages in the U.S. Most mortgages with amortization schedules are simple interest loans.
In contrast, compound interest is often used for long-term investments like 401(k)s and savings accounts. Many credit cards, student loans, and mortgages may also involve compound interest, so it’s important to check the terms before committing.
There’s no strict rule for when simple or compound interest is used, so it’s essential to ask your lender which type applies to your loan.
Examples
Example 1
Jesse is considering a $5,000 car loan with a 3% annual interest rate over five years. How much total interest will he pay?
Using the formula:
A = $5,000 × (1 + 0.03 × 5) = $5,750
Subtracting the principal, Jesse’s total interest is $750.
Example 2
Anna took a simple interest loan for her one-year college tuition of $20,000 at a 5% annual rate. She repays the loan over four years.
The interest is calculated as:
$20,000 × 0.05 × 4 = $4,000
The total repayment amount is:
$20,000 + $4,000 = $24,000
Solutions for Different Variables in Simple Interest Calculations
The simple interest formula can be broken down into four distinct equations, each solving for a different variable.
Calculating Total Interest (Standard Calculation)
$$A=P(1+rt)$$
Calculating the Principal Amount Owed
$$P = \frac{A}{1 + rt}$$
Calculating Interest in Decimal Form
$$r = (\frac{1}{t}) × (\frac{A}{P} – 1)$$
Calculating Interest as a Percentage
$$R = r × 100$$
Calculating the Loan Duration
$$t = (\frac{1}{r}) × (\frac{A}{P} – 1)$$
Example 3: Finding the Loan Duration
Let’s try a reverse calculation to determine the loan term.
Sarah takes out a $10,000 loan at a 5% interest rate. The total amount due, including principal and interest, is $13,500. What is the loan’s duration?
By using the inverse calculation, you can rearrange the formula to solve for time (t). After working through the math, the loan duration is seven years.
$$t = \frac{1}{0.05} × \frac{13,500}{10,000} – 1$$
Key Tips When Calculating Simple Interest
1. Double-Check Your Data
Always review the terms of your contract to ensure you input the correct details. The simple interest calculator offers detailed explanations, helping you understand the factors affecting the outcome.
2. Don’t Assume Interest Will Always Be Fixed
The simple interest calculator provides an estimate of what you might expect to pay, but the actual amount could vary. Some factors, like fluctuating market conditions, can affect the interest rate during the loan term.
3. Watch for Variable Interest Contracts
Certain contracts calculate interest based on market factors, meaning the rate may change over time. Be aware of this possibility as it can impact your final payments.
Summary
Understanding how to calculate simple interest is crucial for both individuals and businesses. However, keep in mind that not all loans use simple interest—many involve compound interest. In those cases, our compound interest calculator can help you determine how interest will accrue on your loans or investments.