# How To Solve Compound Interest And Simple Interest Problems Quickly

## Definition of Simple and Compound Interest

### Compound Interest

The interest charged on the original principal and on the accumulated past interest of a deposit is known as Compound interest.

• Basically A = P (1 + r/n) (nt)

### Simple Interest

Whenever some money is borrowed by someone, then borrower is required to pay an additional amount of money other than the original sum. This additional amount of money is called interest.

• Basically SI = P*R*T/100 ## Type 1: How To Solve Difference between Compound Interest and Simple Interest Quickly

### Question 1.

Rs. 800 is invested in both SI and CI at the same rate of interest for 3 years. If the rate of interest is 20%, find the difference between CI and SI.

Options

A. 120

B. 112.4

C. 102.40

D. 210

#### Solution

We know that,

Difference between CI and SI for 3 years = 3 x P(R)²/(100)² + P (R/100)³

CI – SI = 3*800(20)2/(100)2+800(20/100)3

CI – SI = 102.40

### Question 2.

The difference between SI and CI on Rs. 1200 for 1 year at 10% per annum calculated for 6 months is:

Options

A. Rs. 1

B. Rs. 2

C. Rs. 5

D. Rs. 3

#### Solution

SI = 1200*10*1/100 = 120

CI = 1200 * (1 + 5/100)2 – 1200 = 123

Therefore, their difference = CI – SI = 123 – 120 = Rs. 3

### Question 3.

The CI on a certain amount for 2 years at 10% p.a. is Rs. 525. The SI on the same amount for double the time at half the rate percent p.a. is:

Options

A. 150

B. 50

C. 500

D. 5

#### Solution

Let amount be x

So, P (1+10/100)2 – P = 525

P = 525*100/21

P = 2500

Now, SI = 2500 * 5 * 4/100

SI = 50000/100

SI = 500

## Type 2: Solve Simple Interest and Compound Interest Quickly. Find the amount/time/rate of interest when CI or SI or their difference is given

### Question 1.

The difference between the CI and SI on a certain amount is at 10% p.a. for 3 years is Rs. 31. Find the principal?

Options

A. 1000

B. 3100

C. 310

D. 100

#### Solution

The difference between compound interest and simple interest for three years is 31.
31 = [P (10)2 / (100)2][(300 + 10)/100]

31 = P(31/1000)

On solving further, we get

P = 1000

### Question 2.

If the SI on a sum of money for 2 years at 5% p.a. is Rs. 500, what is the CI on the same sum at the same rate and for the same time?

Options

A. Rs. 512.5

B. Rs 521.5

C. Rs 515.2

D. Rs 215.5

#### Solution

Sum = (500 * 100)/ (2*5)

Sum = 50000/10

Sum = 5000

Amount = 5000 * (1 + 5/100)2

5000 * 1.05 * 1.05 = 5512.5
CI = 5512.5 – 5000

CI = Rs. 512.5

### Question 3.

The difference between CI and SI on a principal of Rs. 15,000 for two years is Rs. 24. What is the annual rate of interest?

Options

A. 16%

B. 4%

C. 8%

D. 6%

#### Solution

CI – SI = PR2  / 1002

On solving further we get,

24 * 100^2= 15000 * R2

R2 = 16

R = 4%