**Go through the given solved examples based on compound interest to understand the concept better.**

**Example 1:**Calculate the Amount and Compound Interest on Rs. 2000 for 2 years at 10% per year.

**Sol:**We need to calculate the value of Amount using this formula:

A = P (1 + R/100)^{T} . Putting the values in this formula, given P = Rs. 2000, R = 10% and T = 2 years

We get the value of A as 2000(1 + 10/100)^{2}. So A = 2000 × (11/10)^{2} = (2000 X 121)/100 = 2420

So, the Amount = Rs. 2420. Hence, Compound Interest = Rs. 2420 – Rs. 2000 = Rs. 420.

**Example 2:**Find the compound interest on Rs. 12,800 for 2 years at per annum.

**Sol:**Here, P = Rs. 12,800, R = 25/2% p.a., T = 2 years

Therefore, A = RS.P(1 + R/100)^{n} = RS.12800[1 + 25/(2 X 100)]^{2}

= RS.12800 (1 + 25/200)^{2} = RS.12800 (1 + 1/8)^{2} = RS.12800 [(8 + 1)/8]^{2}

Hence, the Amount = Rs. 16200

Now, Compound interest = A – P = Rs. 16200 – Rs. 12800 = Rs. 3400

**Example 3:**At what rate percent per annum will a sum of Rs. 10,000 amount to Rs. 14,641 in 4 years compounded annually?

**Sol:** Let the required rate be R% per annum

A = 14641, P = Rs. 10000

We know that A = P (1 + R/100)^{n} 14641 = 10000 (1 + R/100)^{4}

Or 14641/10000 = (1 + R/100)^{4} or (11/10)^{4} = (1 + R/100)^{4}

Or 11/10 = 1 + R/100 or 11/10 -1 = R/100

Or (11 -10)/10 = R/100 or 1/10 = R/100

Or 100/10 = R or 10 = R or R = 10% p.a.

**Example 4:**Calculate the compound interest on Rs. 12000 for 1 years at 10% per annum when compounded half-yearly.

**Sol:**Here, Principal P = Rs. 12000, R = 20% per annum and n = 2 years.

therefore, Amount after 2 years = P (1 + R/200)^{2n}

= RS.12000 X (1 + 10/200)^{2x1}

= RS.12000 X (1 + 1/20)^{2}

= RS.12000 X (21/20)^{2}

= RS.12000 X 21/20 X 21/20

= RS.12000 X 441/400 = RS.13230

therefore, Compound interest = Rs. 13230 – Rs. 12000 = Rs. 1230

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**Example 5:**Shyam deposited in a bank Rs. 7500 for 6 months at the rate of 8% p.a. interest compounded quarterly. Find the amount he received after 6 months.

**Sol:** Here, P = Rs. 7500, R = 8% per annum and n = 6 months = 6/12 = ½ year.

therefore, Amount after 6 months = P(1 + R/400)^{4n}

= RS.7500 X (1 + 8/400)^{4x1/2}

= RS.7500 X (1 + 1/50)^{2}

= RS.7500 X (51/50)^{2}

= RS.7803

**Example 6:** In what time will Rs. 2,560,000 amount to Rs. 2,825,761 at 5% per annum, interest being compounded half-yearly?

**Sol:** Here, Principal P = Rs. 2,560,000, Amount A = Rs. 2,825,761, rate R = 5% per annum

Since, the interest is compounded half-yearly

therefore, A = P(1 + R/200)^{2n} , *where n is the no. of years*

→2,825,761=2,560,000(1 + 5/200)^{2n}

→2,825,761/2,560,000=(41/40)^{2n}

→(41/40)^{4} =(41/40)^{2n}

→2n=4

→n=4/2 years = 2 years

**Example 7:** A sum of Rs. 220 is to be repaid in two equal installments. If the rate of interest be 20 % compounded annually, then what is the value of each installment?

**Sol:** Total sum that has to be paid = Rs.220. Rate of interest = 20%. For compound interest the principal value of all the installments are calculated, added

and then equated with the principal value of loan amount.

Let the value of each installment = x therefore, x/(1 + 20/100)s^{1} + x/(1 + 20/100)^{2} = 220 → x = 144.