Practice Compound Interest questions covering principal, rate, time, annual and half-yearly compounding, and the difference between compound and simple interest for Quantitative Aptitude.
Question 1
Find the compound interest on Rs. 5,000 for 2 years at 10% per annum, interest being compounded annually.
Explanation
Amount = 5000 × 1.1 × 1.1 = 5000 × 1.21 = Rs. 6,050.
Compound interest = 6050 - 5000 = Rs. 1,050.
Compound interest = 6050 - 5000 = Rs. 1,050.
Shortcut Method
Ratio = 11 : 10
5000 →(×11/10)→ 5500 →(×11/10)→ 6050
∴ CI = 6050-5000 = Rs.1,050 ✓
5000 →(×11/10)→ 5500 →(×11/10)→ 6050
∴ CI = 6050-5000 = Rs.1,050 ✓
Question 2
What amount will Rs. 8,000 become in 2 years if invested at 5% per annum compound interest?
Explanation
Compound interest for 2 years means the amount is multiplied by (1 + rate) once for every year.
Amount after year 1 = 8000 × 1.05 = Rs. 8,400.
Amount after year 2 = 8400 × 1.05 = Rs. 8,820.
Amount after year 1 = 8000 × 1.05 = Rs. 8,400.
Amount after year 2 = 8400 × 1.05 = Rs. 8,820.
Shortcut Method
Ratio = 21 : 20 (5%)
8000 →(×21/20)→ 8400 →(×21/20)→ 8820
∴ Amount = Rs.8,820 ✓
8000 →(×21/20)→ 8400 →(×21/20)→ 8820
∴ Amount = Rs.8,820 ✓
Question 3
A sum of Rs. 10,000 is invested at 10% per annum, compounded half-yearly. Find the compound interest earned in 1 year.
Explanation
Compounded half-yearly means the rate per half-year is 5%, applied twice in 1 year.
Amount = 10000 × 1.05 × 1.05 = 10000 × 1.1025 = Rs. 11,025.
Compound interest = 11025 - 10000 = Rs. 1,025.
Amount = 10000 × 1.05 × 1.05 = 10000 × 1.1025 = Rs. 11,025.
Compound interest = 11025 - 10000 = Rs. 1,025.
Shortcut Method
Half-yearly → rate/period = 5%, periods = 2
Ratio = 21 : 20
10000 →(×21/20)→ 10500 →(×21/20)→ 11025
∴ CI = Rs.1,025 ✓
Ratio = 21 : 20
10000 →(×21/20)→ 10500 →(×21/20)→ 11025
∴ CI = Rs.1,025 ✓
Question 4
Find the difference between the compound interest and the simple interest on Rs. 4,000 for 2 years at 5% per annum.
Explanation
Simple interest for 2 years = 4000 × 5 × 2 / 100 = Rs. 400.
Compound interest for 2 years = 4000 × (1.05 × 1.05 - 1) = 4000 × 0.1025 = Rs. 410.
Difference = 410 - 400 = Rs. 10.
Compound interest for 2 years = 4000 × (1.05 × 1.05 - 1) = 4000 × 0.1025 = Rs. 410.
Difference = 410 - 400 = Rs. 10.
Shortcut Method
2-year CI-SI diff = P(r/100)²
= 4000 × (5/100)² = 4000 × 1/400
∴ Difference = Rs.10 ✓
= 4000 × (5/100)² = 4000 × 1/400
∴ Difference = Rs.10 ✓
Question 5
The compound interest on a certain sum of money for 2 years at 10% per annum is Rs. 630. Find the sum.
Explanation
Let the sum be P. Amount factor for 2 years at 10% = 1.1 × 1.1 = 1.21.
Compound interest = P × (1.21 - 1) = 0.21P.
0.21P = 630, so P = 630 / 0.21 = Rs. 3,000.
Compound interest = P × (1.21 - 1) = 0.21P.
0.21P = 630, so P = 630 / 0.21 = Rs. 3,000.
Shortcut Method
CI = P[(1+r/100)²-1]
630 = P × 0.21
∴ P = 630/0.21 = Rs.3,000 ✓
630 = P × 0.21
∴ P = 630/0.21 = Rs.3,000 ✓
Question 6
A sum of Rs. 2,000 amounts to Rs. 2,420 in 2 years, interest being compounded annually. Find the rate of interest per annum.
Explanation
Amount factor for 2 years = 2420 / 2000 = 1.21.
So (1 + r/100)2 = 1.21, giving 1 + r/100 = 1.1, so r = 10%.
So (1 + r/100)2 = 1.21, giving 1 + r/100 = 1.1, so r = 10%.
Shortcut Method
Amount factor = 2420/2000 = 1.21 = (1.1)²
∴ Rate = 10% ✓
∴ Rate = 10% ✓
Question 7
The value of a machine depreciates at the rate of 10% per annum. If its present value is Rs. 8,000, find its value after 2 years.
Explanation
Depreciation reduces the value by 10% each year, so the value is multiplied by 0.9 each year.
Value after 2 years = 8000 × 0.9 × 0.9 = 8000 × 0.81 = Rs. 6,480.
Value after 2 years = 8000 × 0.9 × 0.9 = 8000 × 0.81 = Rs. 6,480.
Shortcut Method
Ratio = 9 : 10 (10% fall)
8000 →(×9/10)→ 7200 →(×9/10)→ 6480
∴ Value = Rs.6,480 ✓
8000 →(×9/10)→ 7200 →(×9/10)→ 6480
∴ Value = Rs.6,480 ✓
Question 8
The population of a town is 20,000. If it increases at the rate of 5% per annum, find the population after 2 years.
Explanation
The population grows by 5% each year, so it is multiplied by 1.05 once for every year.
Population after year 1 = 20000 × 1.05 = 21,000.
Population after year 2 = 21000 × 1.05 = 22,050.
Population after year 1 = 20000 × 1.05 = 21,000.
Population after year 2 = 21000 × 1.05 = 22,050.
Shortcut Method
Ratio = 21 : 20 (5%)
20000 →(×21/20)→ 21000 →(×21/20)→ 22050
∴ Population = 22,050 ✓
20000 →(×21/20)→ 21000 →(×21/20)→ 22050
∴ Population = 22,050 ✓
Question 9
Calculate the compound interest on Rs. 6,000 for 3 years at 10% per annum, interest compounded annually.
Explanation
Amount = 6000 × 1.1 × 1.1 × 1.1 = 6000 × 1.331 = Rs. 7,986.
Compound interest = 7986 - 6000 = Rs. 1,986.
Compound interest = 7986 - 6000 = Rs. 1,986.
Shortcut Method
Ratio = 11 : 10
6000 →(×11/10)→ 6600 →(×11/10)→ 7260 →(×11/10)→ 7986
∴ CI = 7986-6000 = Rs.1,986 ✓
6000 →(×11/10)→ 6600 →(×11/10)→ 7260 →(×11/10)→ 7986
∴ CI = 7986-6000 = Rs.1,986 ✓
Question 10
Find the difference between the compound interest and the simple interest on Rs. 5,000 for 3 years at 10% per annum.
Explanation
Simple interest for 3 years = 5000 × 10 × 3 / 100 = Rs. 1,500.
Amount at compound interest = 5000 × 1.13 = 5000 × 1.331 = Rs. 6,655, so compound interest = Rs. 1,655.
Difference = 1655 - 1500 = Rs. 155.
Amount at compound interest = 5000 × 1.13 = 5000 × 1.331 = Rs. 6,655, so compound interest = Rs. 1,655.
Difference = 1655 - 1500 = Rs. 155.
Shortcut Method
3-year CI-SI diff = P(r/100)²(3+r/100)
= 5000 × 0.01 × 3.1
∴ Difference = Rs.155 ✓
= 5000 × 0.01 × 3.1
∴ Difference = Rs.155 ✓
Question 11
A sum of Rs. 10,000 is invested for 2 years at compound interest, with the rate being 10% for the first year and 20% for the second year. Find the amount at the end of 2 years.
Explanation
Amount after year 1 = 10000 × 1.1 = Rs. 11,000.
Amount after year 2 = 11000 × 1.2 = Rs. 13,200.
Amount after year 2 = 11000 × 1.2 = Rs. 13,200.
Shortcut Method
10000 →(×1.1)→ 11000 →(×1.2)→ 13200
∴ Amount = Rs.13,200 ✓
∴ Amount = Rs.13,200 ✓
Question 12
Find the compound interest on Rs. 10,000 for 6 months at 8% per annum, interest being compounded quarterly.
Explanation
Compounded quarterly at 8% per annum means the rate per quarter is 2%. 6 months = 2 quarters.
Amount = 10000 × 1.02 × 1.02 = 10000 × 1.0404 = Rs. 10,404.
Compound interest = 10404 - 10000 = Rs. 404.
Amount = 10000 × 1.02 × 1.02 = 10000 × 1.0404 = Rs. 10,404.
Compound interest = 10404 - 10000 = Rs. 404.
Shortcut Method
Quarterly → rate/period = 2%, periods = 2
Ratio = 51 : 50
10000 →(×51/50)→ 10200 →(×51/50)→ 10404
∴ CI = Rs.404 ✓
Ratio = 51 : 50
10000 →(×51/50)→ 10200 →(×51/50)→ 10404
∴ CI = Rs.404 ✓
Question 13
In how many years will a sum of Rs. 8,000 amount to Rs. 27,000 at 50% per annum compound interest?
Explanation
Required growth factor = 27000 / 8000 = 3.375.
At 50% per annum, the growth factor per year is 1.5, and 1.53 = 3.375.
So the sum takes 3 years to reach Rs. 27,000.
At 50% per annum, the growth factor per year is 1.5, and 1.53 = 3.375.
So the sum takes 3 years to reach Rs. 27,000.
Shortcut Method
27000/8000 = 3.375
1.5² = 2.25, 1.5³ = 3.375 ✓ match
∴ Time = 3 years ✓
1.5² = 2.25, 1.5³ = 3.375 ✓ match
∴ Time = 3 years ✓
Question 14
The population of a village was 40,000. Due to migration, it decreases at the rate of 5% per annum. Find the population after 2 years.
Explanation
The population falls by 5% each year, so it is multiplied by 0.95 once for every year.
Population after year 1 = 40000 × 0.95 = 38,000.
Population after year 2 = 38000 × 0.95 = 36,100.
Population after year 1 = 40000 × 0.95 = 38,000.
Population after year 2 = 38000 × 0.95 = 36,100.
Shortcut Method
Ratio = 19 : 20 (5% fall)
40000 →(×19/20)→ 38000 →(×19/20)→ 36100
∴ Population = 36,100 ✓
40000 →(×19/20)→ 38000 →(×19/20)→ 36100
∴ Population = 36,100 ✓
Question 15
A sum of money, invested at compound interest, amounts to Rs. 4,410 in 2 years and Rs. 4,630.50 in 3 years. Find the rate of interest per annum.
Explanation
The amount for the 3rd year is obtained from the amount for the 2nd year by multiplying by (1 + r/100) once more.
So (1 + r/100) = 4630.50 / 4410 = 1.05, giving r = 5%.
So (1 + r/100) = 4630.50 / 4410 = 1.05, giving r = 5%.
Shortcut Method
Year3/Year2 = 4630.50/4410 = 1.05
∴ Rate = 5% ✓
∴ Rate = 5% ✓
