The formula for Compound Amount:

P [1+ R/100]^{n} [When money is compounded annually]

= P [1+ R/(2*100)]^{2n} [When money is compounded half-yearly]

= P [1+ R/(12*100)]^{12n} [When money is compounded monthly]

Also, A = CI + P

Where,

P= Principal

R= Rate of Interest

n=Time (in years)

A= Amount

CI= Compound Interest

Solved Questions

Questions 1:

Find the amount if Rs 20000 is invested at 10% p.a. for 3 years.

Solution:

Using the formula: A= P [1+ R/100]^{n}

A = 20000 [1 + (10/100)]^{3}

On Solving, we get A = Rs. 26620

Question 2:

Find the CI, if Rs 1000 was invested for 1.5 years at 20% p.a. compounded half yearly.

Solution:

As it is said that the interest is compounded half yearly. So, the rate of interest will be halved and time will be doubled.

CI = P [1+(R/100)]^{n} - P

CI = 1000 [1+(10/100)]^{3}- 1000

On Solving, we get

CI = Rs. 331

Question 3:

The CI on a sum of Rs 625 in 2 years is Rs 51. Find the rate of interest.

Solution:

We know that A = CI + P

A = 625 + 51 = 676

Now going by the formula: A = P [1+(R/100)]^{n}

676 = 625 [1+(R/100)]^{2}

676/625 = [1+(R/100)]^{2}

We can see that 676 is the square of 26 and 625 is the square of 25

Therefore, (26/25)^{2} = [1+(R/100)]^{2}

26/25 = [1+(R/100)]

26/25 - 1 = R/100

On solving, R = 4%

Question 4:

A sum of money is put on CI for 2 years at 20%. It would fetch Rs 482 more if the interest is payable half yearly than if it were payable yearly. Find the sum.

Solution:

Let the Principal = Rs 100

When compounded annually,

A = 100 [1+20/100]^{2}

When compounded half yearly,

A = 100[1+10/100]^{4}

Difference, 146.41 - 144 = 2.41

If difference is 2.41, then Principal = Rs 100

If difference is 482, then Principal = 100/2.41 × 482

P = Rs 20000.

Question 5:

Manish invested a sum of money at CI. It amounted to Rs 2420 in 2 years and Rs 2662 in 3 years. Find the rate percent per annum.

Solution:

Last year interest = 2662 - 2420 = Rs 242

Therefore, Rate% = (242 * 100)/(2420 * 1)

R% = 10%

Important Formula: To find the difference between SI and CI for 2 years, we use the formula Difference = P[R/100]^{2}

Question 6:

The difference between SI and CI for 2 years at 20% per annum is Rs 8. What is the principal?

Solution:

Using the formula: Difference = P (R/100)^{2}

8 = P[20/100]^{2}

On Solving, P = Rs 200