How to Calculate Interest on a Loan
Typically, using a calculator is the easiest and fastest way to calculate interest on any kind of loan. But if you’re looking to improve your financial literacy or create a detailed financial plan, you can also calculate interest rates by hand. Computing interest on your own can be a little tricky, especially if you aren’t familiar with the basics. Here are a few things you need to know about interest and loans before you break out your calculator:
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What Is Interest?
Interest is how much it costs you to borrow money. If you borrow money from someone, you will be charged a fee until you can pay the entirety of your loan back. The amount of interest charged is usually a certain percentage of the total sum being borrowed.
Think of the money you’re borrowing as any other good or service. Just as you would pay a hairdresser to cut your hair, you have to pay the bank to borrow their money.
Many different types of loans have interest charges, including personal loans, mortgages, and credit cards, as this is a common way that banks and credit card companies make money. Interest rates can fluctuate over time, depending on the current level of demand for loans.
Factors That Affect How Much Interest You Pay
The amount of interest you’re charged can vary from lender to lender, and even from loan to loan. Some of the main factors that may influence your interest rate include:
- Your financial history: Lenders will take your previous and current finances into account, including your credit history, to determine your interest rate. If you have a good credit score, you’ll enjoy lower interest rates because of your reliability and trustworthiness. If you have a poor credit score or a history of defaulting on loans, you’ll be deemed a risky borrower and charged a higher rate.
- Loan amount: Many lenders will use the amount of money you borrow, or the principal balance, to decide upon your interest rate. If you borrow a larger sum, you’ll probably be charged a higher interest rate — and pay more in interest fees. It’s less risky for lenders if you borrow a small amount, so you’ll be charged a lower interest rate.
- Repayment amount: The repayment amount refers to the minimum amount you have to pay on your loan each month or week. There can be serious financial consequences if you fail to make this minimum payment, including damage to your credit score or even legal action. On the other hand, if you make a larger payment than is required, you can pay off your loan more quickly and be charged less in interest.
- Loan term: The amount of time you have to pay back your loan, and the frequency at which you make payments, have a huge impact on interest. If you have a short loan term or frequent payments, you’ll be charged more for each payment, but you’ll be charged less interest over time. If you have a longer loan term or infrequent payments, you’ll have a lower monthly payment but you’ll likely be charged more in interest over the life of your loan. Most loans are paid off monthly, though you may be able to negotiate weekly or biweekly payments with your lender.
Calculating Interest for Different Types of Loans
Naturally, the type of loan you take out can affect your interest rate, as well as how you go about calculating your interest charges.
An amortized loan requires you to make periodic payments on a set schedule, often each month. These payments are applied both toward your interest fees and the amount of your loan. Any loan that must be paid in installments is considered amortized, including personal loans, mortgages, and auto loans.
Your lender will create a schedule for your amortized loan. You’ll pay the same amount each month, but your lender may change how much of that payment goes to the principal loan amount and how much goes toward interest. This provides you with more consistency in your monthly expenses while still paying down your loan.
Generally, your payment will go toward the interest charges first, and the remainder of your payment will be put against the amount you owe on your loan. At the beginning of your loan, you’ll pay more toward interest and less toward your loan balance. As time goes on, your principal balance will decrease, and so will your interest fees, allowing you to pay more toward your loan.
Though similar to taking out a loan, credit cards work much differently when it comes to making payments and charging interest. Credit cards are a form of revolving debt; that is, you have more flexibility in deciding how much debt you take on and how you pay that debt back. During a credit cycle, you can choose how much you’d like to use your card, and at its conclusion, you have the freedom to decide if you want to pay your debt in full or carry a balance into next month’s cycle.
Many credit card companies use compound interest to calculate the fees you owe. Simply put, compound interest is the interest you pay on interest. Depending on the terms of your card, it may be compounded daily, monthly, or annually. Compound interest makes your debt grow more quickly — and makes it more difficult to pay off — because the credit card company charges interest on your loan and on the interest you’ve already accrued.
Luckily, interest is one of the few credit card fees you can avoid entirely if you play your cards right. Credit card companies only charge interest on the balance you carry, so if you pay your balance in full each month, you will never have to pay interest on your credit card. Paying as much as your balance as possible, or making more than the minimum monthly payment, can mitigate the effects of compound interest, but it’s always best to pay off your card completely when you can.
How to Calculate Loan Interest Yourself
Depending on the type of loan you’re looking at, you’ll need to use either the simple interest or compound interest formula to calculate your loan’s interest:
Simple Interest Formula
The simple interest formula is, well, fairly simple. The original formula for calculating interest is A equals P(one plus rt), where:
- A is the total amount owed (your principal balance plus interest);
- P is the principal balance;
- r is the interest rate expressed as a decimal;
- t is the time period of the loan.
Let’s say you have a principal balance of $17,000 on your auto loan. You have an interest rate of 4% and five years to pay off your loan. To calculate the interest you’ll pay on this loan, convert 4% into a decimal, which is 0.04. Then, plug the numbers into the equation:
A equals 17,000(one plus (0.04 times five)) equals 20,400.
$20,400 is the total amount you owe on your loan, including the principal amount and interest. To find the interest you’ll pay on this loan, subtract the principal balance from the total amount owed:
20,400 minus 17,000 equals 3,400.
The total amount of interest you’ll pay on this auto loan is $3,400.
Amortized Loan Formula
The formula for an amortized loan is derived from the simple interest formula. It reads as A equals P((r(one plus r)n divided by (one plus r)n minus one), where:
- A is the amount you have to pay during each period;
- P is the principal balance;
- r is the interest rate you have to pay each month;
- n is the total number of payments you have to make on your loan, expressed in months.
Using the example of a personal loan, let’s say you owe $6,000. You have one year, or 12 months, to repay this loan and your interest rate is 6.5%. After converting your interest rate into a decimal (which is 0.065), plug each value into the equation:
A equals 6,000((one plus 0.065)12 divided by (one plus 0.065)12 minus one) equals 517.78.
Your monthly payment for this loan is $517.78.
With this value, you can go on to determine the amount of interest you’ll pay on your loan. To do so, it’s helpful to create an amortization table, which will show the breakdown of your monthly payments.
|Payment Date||Monthly Payment||Principal Balance||Principal Payment||Interest Payment||Remaining Balance|
You can then add each value in the interest column to figure out how much you’ll spend on interest. In this case, you will have to pay $213 in interest on this loan.
Here’s how you can build your own amortization table:
- Convert the annual interest rate to a monthly one. To do so, divide the interest rate by 12. Continuing with this example, that would be 6.5% divided by 12, or 0.00541%.
- Multiply this monthly rate by the principal balance at the beginning of the month. $6,000 multiplied by 0.0541% equals $32.46 (rounded up to $32.50). This is how much you will pay in interest for the first month of your loan.
- Subtract this interest payment from the monthly payment you previously calculated. $517.78 minus $32.50 equals $485.28, which is the amount that is subtracted from your principal balance. This means your remaining balance is $5,514.72.
- Repeat this process with your new remaining balance for each month for the duration of your loan. For instance, you would begin the calculations for the second month with $5,514.72, as that is your starting balance for that month.
Compound Interest Formula
The compound interest formula is more complicated. It is C equals [P(1 plus r)n minus one], where
- C is the compound interest;
- P is the principal balance;
- r is the annual interest rate, expressed as a percentage;
- n is the frequency at which interest is compounded.
Here, let’s use an interest-earning savings account with a balance of $500 as an example. Your interest rate is 10% and your interest is compounded monthly, or 12 times per year. Convert the annual rate into a monthly one — in this instance, r will be equivalent to 0.10 divided by 12, or 0.00833 — and plug these values into the equation:
C equals [500(one plus (0.10 divided by 12))12 minus one] equals 52.36.
This means you will earn $52.36 in interest on this investment during the course of a year. At the end of 12 months, you will have a total of $552.36 in that account.
While dealing with even a single loan can be difficult, learning how to calculate interest on your own is an easy way to take control of your finances and make sure you’re on the right track. It’s always a good idea to determine the cost of interest before you apply for a loan to ensure it will help, rather than hurt, your financial goals.
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