How to Calculate Simple Interest

When you borrow money, you will usually have to pay interest to the lender. Interest can be calculated using the simple interest method, which means you multiply the loan amount by the interest rate and loan period. The formula for calculating simple interest is $I$ $=$ $P$ $r$ $t$ $.$ ${displaystyle I=Prt.}$ $How to Calculate Simple Interest$ However, banks often charge compound interest on loans. To calculate compound interest, you add the interest to the loan’s annual principal. In the following year, interest will be calculated on the total principal plus interest. Compounding annually is the most common, but it can also be compounded monthly, even weekly, or daily. You can also earn interest (simple or compound interest) on the investments you have put your money in. ^{[1] X Research Source}

Table of Contents

Use the simple interest formula

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Determine the total loan amount. Interest is paid on the total loan amount, aka principal . In case it is an investment, your principal will be the total amount that you have invested. This amount is represented in the simple interest formula by the letter “P.” ^{[2] X Research Source}

For example, let’s say you buy a car that costs $12,000. You paid a $3,000 down payment and borrowed the rest. The principal of your car loan will be $9,000.

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Convert the interest rate to a decimal value. Interest rates are usually expressed as a percentage. You need to divide the percentage rate by 100 to convert it to a decimal. This decimal number will be used in the interest formula. ^{[3] X Research Sources}

For example, if your car loan has an annual interest rate of 7%, you would write this value in the simple interest formula as 0.07.

Tip: Some calculators automatically convert percentages to decimals. You just need to remember to press the percentage button after pressing the number.

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Use the right loan term. Loans typically have a loan term of a certain number of years, denoted by the letter “t” in the simple interest equation. However, in some loans such as car loans, the loan term is usually measured in months. In the simple interest formula, you will have to convert the number of months to the number of years. ^{[4] X Research Sources}

For example, if your car loan has a term of 60 months, you would divide 60 by 12 (the number of months in a year) to get a loan term of 5 years.
Recipe $I$ $=$ $P$ $i$ $n$ ${displaystyle I=Pin}$ ${displaystyle I=Pin}$ Can also be used when you have a loan term in months or weeks. This formula has a slight difference in that the “i” represents the interest rate for each period, and the “n” indicates the period. You would divide the annual interest rate by the number of periods in a year to get the correct value for “i,” then use the total number of months for “n.” Whether adjusting for time periods or interest rates, you will get the same results.

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Find the total amount of interest payable using the formula $I$ $=$ $P$ $r$ $t$ ${displaystyle I=Prt}$ ${displaystyle I=Prt}$ . Once you have the numerical values for the ingredients in the formula, you multiply the numbers together to determine the amount of interest owed over the life of the loan or investment. Continuing the example above, a $9,000 car loan at 7% interest for 5 years: ^{[5] X Source of Research}

$P$ $=$ $9,000 won$ ${displaystyle P=9,000}$ ${displaystyle P=9,000}$
$r$ $=$ $0$ $,$ $07$ ${displaystyle r=0.07}$ ${displaystyle r=0.07}$
$t$ $=$ $5$ ${displaystyle t=5}$ ${displaystyle t=5}$
Interest owed is $3,150. $3,150$ $=$ $9000$ $x$ $0$ $,$ $07$ $x$ $5$ ${displaystyle 3,150=9000\times0.07\times5}$ ${displaystyle 3,150=9000x0.07x5}$ .

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Calculate the total amount owed for the entire loan term. When you pay off your loan with simple interest, you’ll pay back the principal amount borrowed plus the total interest. To calculate the total amount to be paid, you would add the interest to the principal using the formula

I

+

P

{displaystyle I+P}

{displaystyle I+P}

.

Continuing the example above, the total amount you owe is $12,150. $3,150$ $+$ $9,000 won$ $=$ $12.150$ ${displaystyle 3.150+9,000=12,150}$ ${displaystyle 3.150+9,000=12,150}$ .
You can combine both equations if you want to find the total sum over the life of the loan or investment using the formula $A$ $=$ $P$ $($ $first$ $+$ $r$ $t$ $)$ ${displaystyle A=P(1+rt)}$ ${displaystyle A=P(1+rt)}$ .

Compounding

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Start with the initial loan or investment. Similar to simple interest, compound interest is calculated on the principal amount. However, unlike simple interest, compound interest will be added to the principal. In the compound interest formula, the principal is represented by the letter “P” as in the simple interest formula. ^{[6] X Research Source}

For example, let’s say you buy a house for $150,000. You paid $50,000 upfront and mortgaged the rest. Thus, the principal of your mortgage is $100,000.

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Express the annual interest rate as a decimal. Similar to the simple interest formula, the interest rate in the compound interest formula is denoted by the letter “r.” You need to divide this percentage by 100 to find the decimal value. ^{[7] X Research Sources}

For example, if the annual interest rate on a mortgage is 8%, you would write 0.08 in the compound interest formula.

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Determine the term of the loan or investment. In the compound interest formula, the letter “t” represents the number of years the loan or investment is valid. Similar to the simple interest formula, the value of “t” is the number of years, so if the loan term is in months or weeks, you’ll have to change it to years. ^{[8] X Research Sources}

For example, with a 10-year mortgage, you would replace “t” with 10 in the compound interest formula.

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Find the number of periods in which interest will accrue in 1 year. When interest is compounded, it is added to the principal at the end of each period. In the next period, interest will be calculated on the total principal plus interest of the first period. This cycle continues for the life of the loan or until the loan is paid off. ^{[9] X Research Source}

For example, if your mortgage compounding interest is calculated on a monthly basis, it will compound 12 times a year. In the compound interest formula, this value is represented by the letter “n.” ^{[10] X Research Source}
In the case of an investment, the interest will be compounded until the end of the deposit term or until you withdraw the invested capital.

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Calculate the total sum using the compound interest formula. Once you have the numbers for all values, you can determine the total amount that accrues over the life of the loan or investment, including interest. This amount is represented by the letter “A” in the formula. Use the formula A = P (1 + r/n) ^nt . ^{[11] X Research Source}

$P$ $=$ $100,000 won$ ${displaystyle P=100.000}$ ${displaystyle P=100.000}$
$r$ $=$ $0$ $,$ $08$ ${displaystyle r=0.08}$ ${displaystyle r=0.08}$
$n$ $=$ $twelfth$ ${displaystyle n=12}$ ${displaystyle n=12}$
$t$ $=$ $ten$ ${displaystyle t=10}$ ${displaystyle t=10}$
The total amount payable on the mortgage loan will be $221,964. 221.964 = 100,000 (1 + 0.08/12) ¹²⁽¹⁰⁾ . In which, the total profit is $121,964.
Compound interest can be significantly larger than simple interest, especially in the long run. That same loan, if calculated on the simple interest basis, would only pay $80,000 in interest over the life of the loan.

Tip: To find the total interest payable, simply subtract the principal amount from the gross amount. The result will be the total amount of interest payable over the life of the loan or investment.

Advice

Rearrange the formula if you need to calculate principal ( $P$ $=$ $I$ $/$ $CHEAP$ $BILLION$ ${displaystyle P=I/RT}$ ${displaystyle P=I/RT}$ ), interest rate ( $CHEAP$ $=$ $I$ $/$ $P$ $BILLION$ ${displaystyle R=I/PT}$ ${displaystyle R=I/PT}$ ) or loan term ( $BILLION$ $=$ $I$ $/$ $P$ $CHEAP$ ${displaystyle T=I/PR}$ ${displaystyle T=I/PR}$ ).
Don’t confuse interest rate with annual percentage rate (APR). The APR includes fees that are added to interest. When comparing loans, the APR can give you a better idea of how much it will cost to take out a loan. ^{[12] X Research Source}

Steps

Use the simple interest formula

Compounding

Advice

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