Compound Interest: Solved Examples

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

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)s¹ + x/(1 + 20/100)² = 220 → x = 144.