To find Rate when Principal Interest and Time are given

To find Rate when Principal Interest and Time are given | How to Calculate Interest Rate?

Wanna become perfect in various concepts of simple interest? Then here is the perfect guide for you. You can check how to find the principal amount when time interest and rate are given in the previous articles. Now, you can know the step-by-step procedure to find the rate when principal interest and time are given. Follow how to calculate interest rate per annum, month along with the formulas and tips.

Finding the Rate when Principal Interest and Time are given

The interest rate is known as the amount of interest that is due per period. It is calculated as the proportion of the amount deposited, borrowed, and lent. For example, If you borrowed $3000 from a bank and the agreement of the loan stipulates that the rate of interest on the loan is 10%, which means that the borrower must pay the original amount of the loan like $3000 + (10% * 3000) = 3000 + 300 = $3300.

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To find Principal When Time Interest and Rate are Given

Formula to find Rate when Principal, Interest, and Time are given

Consider an example of Mary. Mary took a loan to buy a house from the bank. The amount of money he borrowed from the bank was $7000. According to the bank loan terms, Mary’s loan completes in five years at an interest rate of 6%. He borrowed an initial amount of $7000 which is called the principal amount. In this example, we have the terms of Principal amount, Interest Rate, Interest, Time, etc.

Suppose that we only know the values of Principal Amount, Interest Amount, and Time and we have to find the rate of interest. We know the interest formula as I = P * R * T, if we have all the values and need to find the rate of interest, then we have to rearrange the values. Therefore, the rate of interest can be written as

r = I / PT

in which r is the rate of interest and equals interest rate divided by the principal amount and time period.


Consider an example of finding the rate of interest of the loan when the total interest amount is $20,000 and the principal amount is $7000 over the period of 5 years?

To solve the above calculations, we have to substitute the values in the equation of r = I / PT

r = 20,000 / 7000 * 5

Therefore, the rate of interest is 14.2%

How to Calculate Rate of Interest?

Follow the simple steps provided below while finding the rate of interest. They are as follows:

Step 1: Calculate your interest rate

If you have to calculate the interest rate, you must know the interest formula R = I / PT. Here,


I is the interest amount that is to be paid in the specific time period (year, month etc.)
P is the principal amount before interest
t is the time period involved
r is the interest rate in decimal value
This equation will be used to calculate the basic interest rate.

Step 2: Convert into decimal values

Once you substitute all the values that are required to calculate the rate of interest, you will get the value in decimals. Then, you have to convert the rate of interest by multiplying it by 100. For suppose, the decimal value is .81, it will not help while figuring the interest rate. Therefore, to find the interest rate for .81, you have to multiply it by 100 which is .81 * 100 = 81%

Step 3: Calculate the missing values

If any of the values of the time period, interest amount, principal amount are missing, find those using the formulas,

Interest amount, I = P * R * T
Principal amount, P = I / r * t
Time Period, T = I / P* r

Step 4: Make sure all the values have the same parameter

You have to make sure that all the values of the time period, interest rate are having the same parameter values. If the time period is given in months or days, then you have to convert it to years by dividing it by 12 or 365. The time period which is given must be the same amount of time as the interest paid.

Step 5: Substitute the values in the equation

As we know the rate of interest equation, R = I / PT. Substitute the values of Time, Rate and Interest in the equation.

Suppose that the principal amount is 5000 and the interest is 2000 with a time period of 2 years. Find the rate of interest?

As given,

I = 5000
P = 2000
T = 2 years
The equation is,
R = I / PT
R = 5000 / 2000 * 2
R = 5%
Hence, the rate of interest will be determined in the following steps.

Examples on Calculating Rate of Interest

Problem 1:

A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest?

As given in the question,
Principal = Rs. 12,500
Amount = Rs. 15,500
We know that,
I = A – P
I = 15,500 – 12,500
I = 3,000
We also know that
I = P * R * T / 100
3000 = 12500 * R * 4 / 100
3000 = 125 * 4 * R
R = 3000/125 * 4
R = 3000/500
R = 6%
Therefore, the rate of interest = 6%

Problem 2:

Reha borrows a sum of Rs. 5000 and pays a total amount of Rs. 5500 after 2 years. Find the rate of interest?


As given in the question,
Money borrowed P = Rs. 5000
Amount returned A = Rs 5500
Time T = 2 years
Interest I = Rs 500
We know that,
I = P * R * T / 100
Substitute the values in the above equation,
500 = 5000 * R * 2 / 100
R = 500 * 100 / 5000 * 2
R = 5%
Therefore, the rate of the interest = 5%

Problem 3:

Jerry earned $7000 in interest. He originally deposited $14000 in the account and left it there for 25 years. What is the interest rate he earned?


As given in the question

Interest = 7000
Principal = 14000
Time = 25 years
As we know that,
I = P * R * T
7000 = 14000 * R * 25
7000 = 350000 * R
Divide the equation by 350000
7000 / 350000 = 350000 * R / 350000
R = .02
Multiply it with 100 to convert it into the percentage
∴ R = .02 * 100
R = 2%
Therefore, the rate of interest is 2%

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