Are you eagerly waiting to know the concept of finding principal when time interest and rate are given? If yes, here is the ultimate guide for you. We have curated the best examples which explain how to calculate the principal amount in Simple Interest. Get to know the Principal Definition, Formula, and How to find the Principal when Interest, Time, and rate are given in the later modules.
How to find Principal when Time Interest and Rate are Given?
The principal amount is the total amount that is borrowed or invested. To explain it clearly, we consider the example of Jave. Jave bought a car and as he was in lack of money, he had to take a loan from the bank. He borrowed $6,500 for the car loan. According to the loan terms, Jave has to finish his loan in five years at an interest rate of 8%. The initial amount he borrowed i.e., $6500 is known as the principal amount of the loan.
Not only to loans, but principal amount also applies to deposits or investments in an account. For example, If Jave opens a savings account with the initial deposit of $1000, then the principal amount is $1000.
Principal Amount Formula when Time Interest and Rate are given
In the above example of Jave’s loan, we know the principal amount and we use it to find the amount of interest. Consider that we know the interest rate, amount of time, amount of interest we have to find the principal amount. As know that the interest formula I = PRT, we have to rearrange it to find the principal amount. Therefore, the principal amount can be written as
P = I / (RT)
in which p is the principal amount and equals interest rate divided by the amount of time and interest rate times.
Let’s consider an example of finding the principal amount of the loan where the total interest amount is $18,500 and the rate of annual interest is 6.5% over the period of 12 years.
To solve the above calculations, we have to input the values to the equation, P = I / (RT)
P = 18,500 / 0.065 * 12 = 23718
Therefore, the principal amount is $23,718
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How to Calculate Principal Amount?
Follow the simple steps provided below while finding the Principal Amount. They are as follows
Step 1: Understand the question properly
Once you get the question, understand it properly and know all the terms included in it. We know the equation as
P = I / (RT) where
P is the principal amount
I is the Interest that is paid for month/year etc.
R is the interest rate
T is the time periods (weeks, months, years, etc)
Step 2: Determine the Rate of Interest
In the first step, you have to determine the interest rate. Before you calculate the principal amount, you must know by what rate the principal amount will grow which is the interest rate. You have to convert the interest rate into a decimal by dividing it by 100. If the interest rate is 8%, then we convert it to the decimal as 0.08
Example:Â
Suppose that you gave money to your friend on an understanding that at the end of 4 months he returns you the money back with an interest of 6%. The one-time interest is 6%. You have to convert the interest rate into a decimal, therefore, the interest rate is 0.06.
Step 3: Measure the loan term
In this step, you have to determine the loan length. In most cases, you will agree to return the money in some period of time when you borrow it. The term length must match the interest rate. Suppose that the rate is 3% per year, then the interest must be paid for six months, hence 3% interest must be calculated for 0.5 years.
Step 4: Determine Interest
The interest amount will be mentioned in the problem. It is usually mentioned in Dollars, Rupees, or any currency. Once you know the interest value, check if it is the same scale.
Step 5: Make sure all the terms are on the same scale
Make sure that all the terms are on the correct scale. For example, if you convert it to years to bring them all on the same scale if the time is in months or days. The time that is given must be the same amount of time as the paid interest. Make sure the interest must be calculated as monthly, yearly, or weekly.
Step 6: Substitute the values in the equation
As we know the equation is, P = I / (RT). Substitute all the values of Interest, Rate, and Time in the equation.
For example, Suppose that you have an interest of 2344 for 8% with a time period of 2 years. Find the principal amount?
As given,
I = 2344
R = 0.08
T = 2
The equation is, P = I / (RT)
P = 2344 / (0.88 * 2)
P = 1331.81
Hence, the principal value is determined in the following steps.
Examples on finding Principal When Time and Interest, Rate are Known
Problem 1:
Anand’s bank pays 7.5% simple interest per annum. He has $10,965 in his bank account at the end of the year. How much interest did he earn in the year?
Solution:
Let the starting amount be P
As given in the question,
Rate = 7.5% = 0.075, Time = 1 year
As we know that,
Interest = P * T * R
I = P(1)(0.075)
I = 0.075P
We also know that
Amount = P + I
10965 = P +Â 0.075P
10965 = 1.075P
1.075P = 10965
P = 10965 / 1.075
P = 10200
As we got in the above equation as,
I = 0.075P
I = 0.075 * 10200
I = $765
Thus, the interest he earned in one year = $765
The principal amount = $10200
Problem 2:
The simple Interest on a certain sum of money invested for 5 years at 5 \(\frac { 1 }{ 2 } \) % per annum is $480. What is the principal?
Solution:
As given in the question,
Time, T = 5 years
Rate, R =5 \(\frac { 1 }{ 2 } \) % = 5.5%
Simple Interest I = $480
As we know that,
P = 100 * I / R * T
P = 100 * 480 / 5.5 * 5
P = 48000 / 27.5
P = 1745.45
Therefore, the principal amount is $1745.45
Problem 3:
Find the principal interest which produces simple interest of $675 in 2Â \(\frac { 1 }{ 2 } \) years at 6% per annum?
Solution:
As given in the question,
Simple Interest = $675
Time T = 2 \(\frac { 1 }{ 2 } \) = 2.5 years
Rate R = 6%
As we know the equation,
Principal = 100 * I / R * T
P = 100 * 675 / 6 * 2.5
P = 67500 / 15
P = 4500
Therefore, the principal amount is 4500