# How To Solve Compound Interest And Simple Interest Problems Quickly

## How To solve Compound Interest And Simple Interest Problems Quickly

The Basic Difference Between Simple Interest (SI) and Compound Interest(CI) is that the Simple Interest is the interest calculated on the Principal or sum of amount while Compound Interest is calculated on the principal amount and the previous earned interest also i.e.

SI = $\mathbf{\frac{P × R × T}{100}}$ and  CI =$\mathbf{P (1+ \frac{r}{100})^n}$

### Definition of Simple and Compound Interest

• Compound Interest is the interest charged on the original principal and on the accumulated past interest of a deposit is known as Compound interest.
• Basically , The formula for Amount in Compoun interest , Amount =$\mathbf{P × (1 + \frac{r}{n})^n}$
• Simple Interest is the interest When 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 , the formula for Simple Interest, SI  = $\mathbf{\frac{P * R * T}{100}}$

### 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 =  $\mathbf{3 × \frac{P × (R)^2}{(100)^2} + P × (\frac{R}{100})^3}$

CI – SI= $\mathbf{3 × \frac{800 × (20)^2}{(100)^2} + 800 × (\frac{20}{100})^3}$

On Solving ,

CI – SI = 102.40

Correct option: C

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 = $\frac{1200 * 10 * 1}{100}$= 120

CI = 1200 $1200 (1+ \frac{5}{100})^{n} – 1200$ = 123

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

Correct option: D

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,   $P (1+ \frac{10}{100})^{2} – P$ = 525

P =  $\frac{525 × 100 }{21}$

P = 2500

Now, SI =$\frac{2500 × 5 × 4 }{100}$

SI = $\frac{50000 }{100}$

SI = 500

Correct option: C

### 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.

Difference = $\frac{P × (R)^2}{(100)^2} × \frac{(300 + R) }{100}$

31 = $\frac{P × (10)^2}{(100)^2} × \frac{(300 + 10) }{100}$

31 = $P × \frac{31 }{1000}$

On solving further, we get

P = 1000

Correct option: A

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 = $\frac{500 × 100 }{2 × 5}$

Sum = $\frac{50000 }{10}$

Sum = 5000

Amount =  $5000 (1+ \frac{5}{100})^{2}$

5000 × 1.05 × 1.05 = 5512.5

CI = 5512.5 – 5000

CI = Rs. 512.5

Correct option: A

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 = $\frac{P × (R)^2}{(100)^2}$

On solving further we get,

24 × $(100)_{2}$= 15000 × R2

R2 = 16

R = 4%

Correct option: B