The formula given below can be used to find the difference between compound interest and simple interest for two years.
The above formula is applicable only in the following conditions.
1. The principal in simple interest and compound interest must be same.
2. Rate of interest must be same in simple interest and compound interest.
3. In compound interest, interest has to be compounded annually.
Example 1 :
The difference between the compound interest and simple interest on a certain investment at 10% per year for 2 years is $631. Find the value of the investment.
Solution :
The difference between compound interest and simple interest for 2 years is 631.
Then we have,
P(R/100)2 = 631
Substitute R = 10.
P(10/100)2 = 631
P(1/10)2 = 631
P(1/100) = 631
Multiply both sides by 100.
P = 631 x 100
P = 63100
So, the value of the investment is $63100.
Example 2 :
The compound interest and simple interest on a certain sum for 2 years is $ 1230 and $ 1200 respectively. The rate of interest is same
for both compound interest and simple interest and it is compounded annually. What is the principal ?
Solution :
To find the principal, we need rate of interest. So, let us find the rate of interest first.
Step 1 :
Simple interest for two years is $1200. So interest per year in simple interest is $600.
So, C.I for 1st year is $600 and for 2nd year is $630.
(Since it is compounded annually, S.I and C.I for 1st year would be same)
Step 2 :
When we compare the C.I for 1st year and 2nd year, it is clear that the interest earned in 2nd year is 30 more than the first year.
Because, in C.I, interest $600 earned in 1st year earned this $30 in 2nd year.
It can be considered as simple interest for one year.
That is, principle = 600, interest = 30
I = PRT/100
30 = (600 x R x 1)/100
30 = 6R
Divide both sides by 6.
5 = R
So, R = 5%.
Step 3 :
The difference between compound interest and simple interest for two years is
= 1230 - 1200
= 30
Then we have,
P(R/100)2 = 30
Substitute R = 5.
P(5/100)2 = 30
P(1/20)2 = 30
P(1/400) = 30
Multiply both sides by 400.
P = 30 x 400
P = 12000
So, the principal is $12000.
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Q.1.The difference in simple interest and compound interest on a certain sum of money in 2 years at 10 % p.a. is Rs. 50. The sum is
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- RD Sharma Solutions Class 8 Mathematics Solutions for Compound Interest Exercise 14.2 in Chapter 14 - Compound Interest
- What is the difference between compound interest and simple interest for 2 years on the sum of?
- What is the difference between simple interest and compound interest for a period of 2 years at the rate of 10% per annum on the sum of dollar 60000?
- What is the difference between simple interest and compound interest for a period of 2 years at a rate of 10%?
- For what sum of money the difference between simple interest and compound interest for 2 years at 5% per annum equals to Rs 50?
a) Rs. 10000
b) Rs. 6000
c) Rs. 5000
d) Rs. 2000
e) None of these
Q.2. The difference in simple interest and compound interest on a certain sum of money in 2 years at 18 % p.a. is Rs. 162. The sum is
a) Rs. 4000
b) Rs. 5200
c) Rs. 4250
d) Rs. 5000
e) None of these
Q.3. The compound interest on a certain sum of money for 2 years is Rs. 208 and the simple interest for the same time at the same rate is Rs. 200. Find the rate %.
a) 5 %
b) 6 %
c) 7 %
d) 4 %
e) 8 %
Q.4.The difference between compound interest and simple interest on a certain sum for 2 years at 10 % is Rs. 25. The sum is
a) Rs. 1200
b) Rs. 2500
c) Rs. 750
d) Rs. 1250
e) Rs. 2000
Q.5.The simple interest on a certain sum for 3 years in Rs. 225 and the compound interest on the same sum for 2 years is Rs. 165. Find the rate percent per annum.
a) 20 %
b) 2.5 %
c) 5 %
d) 15 %
e) 7.5%
Q.6.The simple interest on a sum of money for 2 years is Rs. 150 and the compound interest on the same sum at same rate for 2 years is Rs. 155. The rate % p.a. is
a) 16 %
b) 20/3 %
c) 12 %
d) 10 %
e) None of these
Q7.Mihir’s capital is 5/4 times more than Tulsi’s capital. Tulsi invested her capital at 50 % per annum for 3 years (compounded annually). At what rate % p.a. simple interest should Mihir invest his capital so that after 3 years, they both have the same amount of capital?
a) 20/3 %
b) 10 %
c) 50/3 %
d) 1.728 %
e) None of these
Q8.The difference in simple interest and compound interest on a certain sum of money in 3 years at 10 % p.a. is Rs. 372. The sum is
a) Rs. 8000
b) Rs.9000
c) Rs. 10000
d) Rs. 12000
e) None of these
Q9.Sahil’s capital is 1/6 times more than Chaya’s capital. Chaya invested her capital at 20 % per annum for 2 years (compounded annually). At what rate % p.a. simple interest should Sahil invest his capital so that after 2 years, they both have the same amount of capital?
a) 10%
b) 11 5/7%
c) 20%
d) 13 5/7%
e) None of these
Q10.The difference in simple interest and compound interest on a certain sum of money in 3 years at 20 % p.a. is Rs. 640. The sum is
a) Rs. 5000
b) Rs. 8500
c) Rs. 8250
d) Rs. 6000
e) None of these
Jump to
- Compound Interest Exercise 14.1
- Compound Interest Exercise 14.2
- Compound Interest Exercise 14.3
- Compound Interest Exercise 14.4
- Compound Interest Exercise 14.5
- Rational Numbers
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- Playing with Numbers
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- Data Handling Probability
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RD Sharma Solutions Class 8 Mathematics Solutions for Compound Interest Exercise 14.2 in Chapter 14 - Compound Interest
Question 36 Compound Interest Exercise 14.2
The difference between the compound interest and simple interest on a certain sum for 2 years at 7.5% per annum is Rs. 360. Find the sum.
Answer:
Given,
Time = 2 years
Rate = 7.5 % per annum
Let principal = Rs P
Compound Interest (CI) – Simple Interest (SI) = Rs 360
C.I – S.I = Rs 360
By using the formula,
P [(1 + R/100)^n - 1] – (PTR)/100 = 360
P [(1 + 7.5/100)^2 - 1] – (P(2)(7.5))/100 = 360
P[249/1600] – (3P)/20 = 360
249/1600P – 3/20P = 360
(249P-240P)/1600 = 360
9P = 360 × 1600
P = 576000/9
= 64000
∴ The sum is Rs 64000
Video transcript
hello everybody welcome to leader learning my name is rajna chaudhary and we have to write this statement in the equation form it is written that write equation for the statements for these statements so statement is one fourth of a number x minus g minus four gives four so one fourth of a number x would be one fourth of x that mean the value of this part is 1 by 4 of x then we have to minus 4 from it so let's minus 4 from it so minus 4 and gives gives means is equal to 4 so this is the equation for the statement we can write it like that at the place of off we can write multiply then minus 4 is equal to 4. we can also write it like x upon 4 minus 4 is equal to 4. so this is the form of equation for the statement i hope you understand the method see you in my next video don't forget to like comment and subscribe leader learning channel thank you for watching
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What is the difference between compound interest and simple interest for 2 years on the sum of?
The difference between the compound interest and simple interest on a certain sum for 2 years at 7.5% per annum is Rs. 360.
What is the difference between simple interest and compound interest for a period of 2 years at the rate of 10% per annum on the sum of dollar 60000?
The difference between compound interest and simple interest on a sum of 2 years at 10% per annum, when the interest is compounded annually is Rs. 16. If the interest were compounded half yearly, the difference in two interests would be.
What is the difference between simple interest and compound interest for a period of 2 years at a rate of 10%?
The difference between C.I and S.I for 2 years at 10% per annum is Rs. 50 .
For what sum of money the difference between simple interest and compound interest for 2 years at 5% per annum equals to Rs 50?
Hence, the sum is Rs. 6000.