To find Time when Principal Interest and Rate are given

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

Confused about the concept of finding time in simple interest? Here, we are providing detailed information to find time when principal interest and rate are given. Follow the time definition, formula, and conversion of months and days into years to solve simple interest problems, etc. Check the later modules to know the examples and step-by-step procedure to solve the time problems when principal, interest, and rate are given.

To find Time when Principal Interest and Rate are given

Time in simple interest is considered as the starting period when the money is borrowed to the period of time by which the money should be returned with the additional amount of interest. It is also called the deadline or term.

To explain it in clear, we consider an example, Maria was doing her Masters and she was in lack of money, so she thought of taking the student loan of $20,000 from the bank. The interest rate for the loan is 4% and the interest amount she has to pay by the end of term is $8000. The time period by which she has to repay the loan is 5 years which is known as time.

Apart from loans, the time period is also valid for deposits, investments, borrows etc. For example, If Maria opens a fixed deposit for a fixed tenure of 10 years. Then the tenure is known as the time period.

Time Formula when Principal, Interest, and Rate are given

In the above example of Maria’s student loan, we know the time period and we use it to find the simple interest. Consider that we know the principal amount, interest amount, and rate of interest we have to calculate the time period, As we know the interest formula I = P * R * T / 100, we have to rearrange to find the time period.

Therefore, the time can be written as
T = (100 * I) / (P * R)
in which T is the time and equals 100 and interest divided by the principal amount and rate of interest.

Let us consider an example of finding the time period of the loan where the principal amount is $6000, the interest amount is $3600 and the rate of interest is 6%

To solve the above calculations, we have to substitute the values in the equation, T = (100 * I) / (P * R)
T = (100 * 3600) / (6000 * 6)
T = 360000 / 36000
T = 10 years
Therefore, the time is 10 years

Read More Articles

What is Simple Interest Worksheet on Simple Interest Worksheet on Factors Affecting Interest
Simple Interest when time is given in months and days To find Rate when Principal Interest and Time are given To find Principal When Time Interest and Rate are Given

How to Calculate Time in Simple Interest?

You have to follow a few steps to calculate time in simple interest. The steps are as follows:
Step 1: Understand the question properly
Once you know the question, understand it clearly and know the terms included in it. We know the equation as,
T = (100 * I) / (P * R)
T is the time period(year/month)
I is the interest amount paid for year/month
P is the principal amount
R is the rate of interest
Step 2: Determine the Principal amount
In the first step, you have to determine the principal amount. Before calculating the time period, you must know the principal amount by which the interest rate will grow. It is the amount that is initially credited or invested.
Step 3: Determine the interest rate
Next, you have to determine the interest rate. If the interest rate is in decimal value, then you have to convert it to percentages by multiplying it by 100. For suppose, you took $5000 from your friend and agreed upon the interest of 6% and the interest amount is $150. Then 6% is the interest rate.
Step 4: Determine the interest amount
You have to find the interest amount also. As given in the above example, the interest amount is $150.
Step 5: Substitute the values in the equation
As we know the equation, T = (100 * I) / (P * R). Substitute all the values of principal, interest rate and interest amount in the equation.
As given in the above example, the values are
P = $5000
I = $150
R = 6%
The equation is,
T = (100 * I) / (P * R)
T = (100 * 150) / (5000 * 6)
T = 15000 / 30000
T = 0.5 years

Conversion of Years into Months and Days

If we get the time period in years and want to convert it into months or days, then there is a technique to follow. If you want to convert the time into months, then you have to multiply it by 12 and if you want to convert it to days, then you have to multiply it by 365, then you get the desired time period in months or days.

For example, you took $5000 from your friend and agreed upon the interest of 6% and the interest amount is $150. Then 6% is the interest rate. Find the time period in months?
As given,
P = $5000
I = $150
R = 6%
The equation is,
T = (100 * I) / (P * R)
T = (100 * 150) / (5000 * 6)
T = 15000 / 30000
T = 0.5 years
To find the time in months, we have to multiply it with 12
Therefore, time = 0.5 * 12 = 6
Hence, the time period is 6 months

Example Problems to find Time When Principal, Interest and Rate are Given

Problem 1:
At what time will a loan of $6500 generate a simple interest of $1300 at the rate of 2.5%?
Solution:
As given in the question,
Principal, P = $6500
Simple Interest, I = $1300
Rate of Interest = 2.5%
As we know the formula,
T = (100 * I) / (P * R)
T = 100 * 1300 / 6500 * 2.5
T = 130000 / 16250
T = 8
Therefore, the time period is 8 years

Problem 2:
In how much period of time would Rs. 11,500 become Rs. 14,605 at a Simple Interest rate of 9% per annum. Define the time period in days?
Solution:
As given in the question,
Principal P = 11,500
Amount A = 14,605
Rate = 9%
Amount = SI + P
14605 = SI + 11500
SI = 3105
As we know that,
SI = P * R * T / 100
T = SI * 100 / P * R
T = 3105 * 100 / 1500 * 9
T = 3 years
To convert years into days, we have to multiply it with 365
T = 3 * 365
T = 1095
Therefore, the time period is 1095 days

Problem 3:
In how much time will Rs. 1200 mount to Rs. 1726 at 9% per annum simple interest. Find the time period in months?
Solution:
As given in the question,
Amount A = 1726
Principal P = 1200
Rate R = 9%
Simple Interest = Amount – Principal
SI = 1726 – 1200
SI = 526
We know that,
Time = 100 * SI / P * R
T = 100 * 526 / 1200 * 9
T = 52600 / 10800
T = 4.8 years
To convert the time of years into months, multiply it with 12
T = 4.8 * 12
T = 57.6 months
Therefore, the time period in months = 57.6 months

Leave a Comment

Scroll to Top
Scroll to Top