Interest is a profit of an investment. There are many ways to calculate the interest. The quick method of calculating the interest charge on a loan is called simple interest. The sum of money invested is called the principal which is denoted by 'P'. The money earned by the principal is called the interest (I) and is earned at a rate known as the interest rate (R).
Example
Let us consider an investment on simple interest terms of Rs 200 invested for 2 years at 15% per annum ( p.a). Each year the investor will receive interest equal to 15% of the principal. Interest received at the end of the first year = 15% of Rs 200 = \(\frac{15}{100}\)x 200 = Rs.30
Similarly, interest received at the end of the second year = Rs 30.
The total interest ( I ), received = Rs 30 + Rs 30 = Rs 60
The investor also gets the principal of Rs 200 back at the end of the second year.
In the above example, interest ( I ) = 15 % of Rs 200 x 2
Interest ( I ) = 15 % of Rs 200 x 2
= \(\frac{15}{100}\)x 200 x 2
Replace, \(\frac{15}{100}\) by R, Rs 200 by P and 2 by T
I = R x P xT
Thus, I = PTR
Hence, if Rs P is invested at the rate of R% per annum for T years, then the interest, Rs I, earned is given by I = PTR
Also, P = \(\frac{I}{TR}\), T = \(\frac{I}{PR}\) and R = \(\frac{I}{PT}\)
The sum of principal and interest is called amount ( A )
Thus, A = P + I
A = P +PTR
A = P (1 + TR )
So, P = \(\frac{A}{1+TR}\)
Examples
Solution,
Given information,
Principal amount (P)= Rs 76,00
Time (T) = 3 years
Interest (I) = Rs 1,254
Rate (R) =?
Formula, R = \(\frac{I×100}{PT}\)
(R) = \(\frac{1254×100}{7600×3}\)
= 5.5%
Solution:
Given information,
Time (T) = 7 years
Interest (I) =Rs 4200
Rate (R) = 6%
Principal (P) = ?
Formula, P= \(\frac{I×100}{TR}\)
∴ (P) = \(\frac{4200×100}{7×6}\)
= \(\frac{420000}{42}\)
= Rs 10,000
∴ She has to Rs 10,000 now.
Solution:
Given inforamtion,
Principal (P) = Rs 3,000
Rate (R) = 5% = \(\frac{5}{100}\) p.a
We have,
Simple Interest (I) =P× T× R
= Rs 3,000× 4× \(\frac{5}{100}\)
=Rs 600
Hence , She will pay Rs 600 at simple interest.
Solution:
Given information,
Principal(P) = Rs 12,000
Rate (R) = 18% = \(\frac{18}{100}\) p.a
Time (T) = 9 Months = \(\frac{9}{12}\) years
We have,
Simple Interest (I) = P× T× R
= Rs 12,000× \(\frac{18}{100}\)× \(\frac{9}{12}\)
= Rs 1,620
So, Suzu paid Rs 1,620 in interest.
Solution:
Given information,
Principal (P) = Rs 3000
Since, we are doubling Rs 3000, we made an additional Rs 3000 on this investment, which is the interest.
So, Interest (I) = Rs 3000
Rate (R)= 20% = \(\frac{20}{100}\) p.a
We have,
Time (T) = \(\frac{3000}{3000 \times \frac{20}{100}}\)
= \(\frac{100}{20}\)
Hence, It takes 5 years to double the amount.
Solution:
Given information,
Time (T) = 2 Years
Simple Interest (I) = Rs 100
Rate (R) = 8% =\(\frac{8}{100}\)
We have,
P = \(\frac{I}{T×R}\)
= \(\frac{100}{2\times\frac{8}{100}}\)
= \(\frac{10000}{16}\)
= 625
Hence, principal is Rs 625
Solution:
Given information,
Principal (P) =Rs 100
Interest (I) =Rs 200
Time (T) = 3 years
We have,
R = \(\frac{I}{P×T}\)
= \(\frac{200}{100×3}\)
= \(\frac{200}{300}\)
= 66%
Hence, The interest rate is 66%
Solution:
Given Information,
Rate (R) =2%
Time (T) = 3 years
Interest (I)= Rs 120
Principal (P) = ?
We know ,
P =\(\frac{I×100}{T×R}\)
= Rs \(\frac{120×100}{T×R}\)
= Rs 2000
∴ Rs 2000 amount should be invested.
Solution:
Given information,
Principal (P) = Rs 1500
Time (T) = 4 years
Interest (I) = Rs 200
Rate (R) =?
We know,
Interest Rate (R) = \(\frac{I×100}{P×T}\)
= \(\frac{I×100}{1500×4}\)
=\(\frac{50}{15}\)
=\(\frac{10}{3}\)%
= 3 \(\frac{1}{3}\) %
∴ Interest Rate (R) = 3 \(\frac{1}{3}\) %
Solution:
Given information,
Principal(P)= Rs 7,200
Time (T) = 5 Years
Interest(I) = Rs 1080
Interest Rate(R) = ?
We know,
R = \(\frac{I\times100}{PT}\)
= \(\frac{1080\times100}{7100\times5}\)
Hence, Interest Rate(R) = 3%
Find the value (T) Time:
Principal(P) =Rs 1250
Rate(R) = 13%
Interest(I) = Rs 650
Time(T) =?
Find the value of Interest Rate(R)?
Principal(P) = rS 1460
Time(T) = 30 Months
Interest(I) = Rs 292
Rate =?
Find the difference between compound interest and simple interest on Rs 12,000 and in 1(frac{1}{2}) years at 10% compounded yearly.
Saroj invested Rs 8,000 for 3 years at a simple interest rate of 8% per annum. He also invested the same sum for the same period at a compound interest rate of 7(frac{1}{2})% per annum, how much more would he have received after 3 years?
Find the sum of money invested, if the difference between the compound interest and simple interest for 2 years at 9% per annum is Rs12960.
Calculate the simple interest on Rs 600 for 2(frac{1}{2})years at 4% per annum.
Renu took Rs 400 from Saroj and returned him Rs 3000 after 5 years. Find the annum rate of interest in percent.
What will be the amount on Rs 900 at 5 % per annum for 6 years?
Sapana took a loan of Rs 850 from Renu for 3 years at 10 % per annum. After 3 years Sapana paid back the loan by giving Rs 900 in cash and a New Bag. What was the price of the New Bag?
What is the difference between the compound interest and simple interest for 3 years that become Rs 930 at 10%.
Find the Amount (A)?
Principal(P) = Rs 50,000
Time(T) =7 Years
Rate (R) =3%
Amount(A) = ?
Find the Principal (P).
Rate (R) = 9%
Time (T) = 9 Years
Interest (I) = Rs 810
Principla =?
Find the Simple Interest of the following?
Principal(P)=Rs 500
Rate (R) = 3%
Time (T) = 3 Years
Simple Interest (S.I) =?
Find the value of Time (T)?
Principal (P) = Rs 4500
Rate (R) = 4%
Interest (I) = Rs 900
Time (T) =?
To get Rs 56,610 in 4 months, how much amount should be invested now at the rate of 6 %?
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Mar 10, 2018
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Drishya
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