Simple Interest Calculator A = P(1 + rt)
Calculator Use
A = P(1 + rt)
The formula for calculating simple interest plus principal is A = P(1 + rt). Here, A is the total accrued amount, which is principal plus interest or P + I, so interest is I = Prt.
In calculating simple interest P is the principal amount of money invested at an interest rate R% per period for t, the number of time periods.
For these calculations the interest rate r is in decimal form, so note that r is R% divided by 100. Just take your interest rate as a percentage and divide by 100. Also r and t are in the same units of time, typically years.
How to Calculate Simple Interest Plus Principal
The most efficient way to calculate simple interest plus principal is to complete the calculation in one step with the simple interest equation A = P(1 + rt), where
- A = Total accrued amount (principal + interest)
- P = Principal amount
- R = Rate of interest per year as a percent
- r = Rate of interest per year as a decimal: r = R%/100
- t = Time period
- I = Simple interest
You could also calculate simple interest only with the formula I = Prt, where I is interest, P is principal, r is interest rate as a decimal, and t is time period. You then need to add the interest to the original principal amount to get the total interest plus principal. So doing it this way involves multiple steps.
If you would like to calculate only the simple interest amount without adding in principal use the CalculatorSoup® Simple Interest Calculator.
What Does Simple Interest Mean?
Simple interest is different from compound interest -- when interest that accumulates is added back into the balance of the investment principal. With compound interest there is a sub-calculation for each time period that includes interest rolling back into the investment balance.
You should use the simple interest formula A = P(1 + rt) to calculate non-compounded interest plus principal on a savings amount. The interest earned is not added back into the principal balance for subsequent interest calculations.
If you do a simple interest calculation on a savings or investment account, keep in mind the total interest accrued over time will change if you make extra deposits or withdrawals.
Using the Simple Interest Calculator
This simple interest calculator can find the total principal plus interest, principal only and interest only. It can also calculate the simple interest rate, or time period in days, weeks, months, quarters and years. Input any three variables of total amount, principal, interest rate or time period and the calculator can find the missing variable.
How to Calculate the Simple Interest Rate
The formula to find the simple interest rate is r = (1/t)(A/P - 1). You can see that we have rewritten the equation to solve for interest rate r. We have also rewritten the simple interest equation for other variables in this list of formulas to calculate any variable in the simple interest equation.
Here is an example of how to find the simple interest rate. Say you want to have an investment where at the end of the investment time period the total principal plus interest A = $26,800. The investment term is t = 4 years, and the original principal P = 22,000. What is the simple interest rate that you need to end up with $26,800?
Using the formula for the simple interest rate r = (1/t)(A/P - 1), plug the known variables into the equation.
r = (1/t)(A/P - 1)
r = (1/4)((26,800 / 22,000) - 1)
r = (0.25)(1.218 - 1)
r = (0.25)(0.218)
r = 0.0545
Multiply r by 100 to get R as a percentage
R = 0.0545 * 100
R = 5.45%
So for a total accrued amount of $26,800 with an original principal of $22,000 and a term of 4 years, the simple interest rate you'll need is 5.45%.
How to Calculate Simple Interest for Months
At some point you may need to calculate simple interest for a period of months rather than years. You would use the same simple interest formula A = P( + rt), but you first need to convert your number of months into an equivalent number of years. Just divide months by 12 because there are 12 months per year.
Let's do an example of finding simple interest for a period of 9 months. Say you're getting a short-term CD for $10,000, and the rate is 4% with no compounding. What is the amount of simple interest that you will earn?
Using the formula for simple interest plus principal A = P(1 + rt), plug the known variables into the equation.
A = P(1 + rt)
Convert months to its equivalent in years: 9 / 12 = 0.75
A = 10,000(1 + (0.04 * 0.75))
A = 10,000(1 + 0.03)
A = 10,000(1.03)
A = 10,300
Since your total principal plus interest is $10,300, subtract the original principal of $10,000 to get the amount of interest:
Simple Interest = 10,300 - 10,000 = $300
Just remember to divide your number of months by 12 to get the number of years if you're doing this calculation by hand. The Simple Interest Calculator above lets you plug in months so we do the conversion for you.
How to Calculate Simple Interest for Days
What if you need to calculate simple interest given a period of days rather than years? Use the simple interest formula A = P(1 + rt), but first convert the number of days into the equivalent number of years. Divide the number of days by 365 since there are 365 days per year.
Here is an example of finding simple interest for a period of 548 days. This is a short-term investment of $10,200 with a rate of 3.5% with no compounding. What is the amount of simple interest that you will earn?
Use the formula for simple interest and plug the known variables into the equation.
A = P(1 + rt)
Convert days to its equivalent in years: 548 / 365 = 1.50137
A = 10,200(1 + (0.035 * 1.50137))
A = 10,200(1 + 0.052548)
A = 10,200(1.052548)
A = 10,735.99
Since your total principal plus interest is $10,735.99, subtract the original principal of $10,200 to get the amount of interest:
Simple Interest = 10,735.99 - 10,200 = $535.99
Just remember to divide your number of days by 365 to get the number of years if you're doing this calculation by hand. The Simple Interest Calculator above lets you plug in days so we do the conversion for you.
About the Simple Interest Formula Used by This Calculator
The formula for calculating simple interest plus principal is A = P(1 + rt).
Here, A is the total accrued amount, which is principal plus interest or P + I, so A = P + I.
The formula for calculating interest is I = Prt.
You can substitute Prt for I in the original equation to get A = P + Prt.
Factor out the P to get the equation for principal plus simple interest: A = P(1 + rt).
Equations to Find the Missing Variable in Simple Interest Calculations
- Calculate Total Amount Accrued (Principal + Interest), solve for A
- A = P(1 + rt)
- Calculate Principal Amount, solve for P
- P = A / (1 + rt)
- Calculate rate of interest in decimal, solve for r
- r = (1/t)(A/P - 1)
- Calculate rate of interest in percent
- R = r * 100
- Calculate time, solve for t
- t = (1/r)(A/P - 1)
- Calculate Simple Interest, solve for I
- I = A - P
Time Conversion Factors Used in this Simple Interest Plus Principal Calculator
This calculator uses conversion factors that correspond to a typical 365-day year.
In simple interest calculations that involve months, we divide 365 by 12 to get the average of 30.4167 days per month.
For simple interst calculations involving quarters, we divide 365 by 4 to get 91.25 days per quarter.