1. Find the compound interest on ₹20,000 at 15% per annum for 3 years.
Solution:
P = ₹20,000, R = 15%, T = 3 years
A = P (1 + R/100)^T
= 20000 × (1 + 15/100)³
= 20000 × (1.15)³
= 20000 × 1.520875
= ₹30,417.50
CI = A – P
= 30417.50 – 20000
= ₹10,417.50
Answer: ₹10,417.50
2. Find the compound interest on ₹5000 at 8% per annum for 3 years.
Solution:
P = ₹5000, R = 8%, T = 3 years
A = 5000 × (1 + 8/100)³
= 5000 × (1.08)³
= 5000 × 1.259712
= ₹6,298.56
CI = A – P
= 6298.56 – 5000
= ₹1,298.56
Answer: ₹1,298.56
3. Find the compound interest on ₹8000 at 5% per annum for 3 years.
Solution:
P = ₹8000, R = 5%, T = 3 years
A = 8000 × (1 + 5/100)³
= 8000 × (1.05)³
= 8000 × 1.157625
= ₹9,261
CI = A – P
= 9261 – 8000
= ₹1,261
Answer: ₹1,261
4. Find the amount and the compound interest on ₹2500 at 15% per annum for 2 years.
Solution:
P = ₹2500, R = 15%, T = 2 years
A = 2500 × (1 + 15/100)²
= 2500 × (1.15)²
= 2500 × 1.3225
= ₹3,306.25
CI = A – P
= 3306.25 – 2500
= ₹806.25
Final Answer: Amount = ₹3,306.25, CI = ₹806.25
5. Find the compound interest on ₹4000 for 1 ½ years at 10% per annum.
Solution:
For 1.5 years, we can calculate interest for 1 year and then for the next half year separately.
After 1st year:
A1 = 4000 × (1 + 10/100) = 4000 × 1.10 = ₹4,400
For the next ½ year: This ₹4,400 becomes the new principal.
Interest for half year = (4400 × 10 × 0.5) / 100 = ₹220
Amount after 1.5 years = 4400 + 220 = ₹4,620
CI = 4620 – 4000 = ₹620
Answer RS620
6. Find the compound interest on ₹5000 at 6% per annum for 3 years.
Solution:
P = ₹5000, R = 6%, T = 3 years
A = 5000 × (1 + 6/100)³
= 5000 × (1.06)³
= 5000 × 1.191016
= ₹5,955.08
CI = A – P
= 5955.08 – 5000
= ₹955.08
Answer: ₹955.08
7. Calculate the amount if ₹18,000 is invested at 15% p.a. compounded annually for 3 years.
Solution:
P = ₹18,000, R = 15%, T = 3 years
A = 18000 × (1 + 15/100)³
= 18000 × (1.15)³
= 18000 × 1.520875
= ₹27,375.75
Answer: ₹27,375.75
8. Calculate the amount if ₹12,000 is invested at 12% p.a. compounded annually for 2 years. Also, the compound interest.
Solution:
P = ₹12,000, R = 12%, T = 2 years
A = 12000 × (1 + 12/100)²
= 12000 × (1.12)²
= 12000 × 1.2544
= ₹15,052.80
CI = A – P
= 15052.80 – 12000
= ₹3,052.80
Amount = ₹15,052.80, CI = ₹3,052.80
9. Calculate the compound interest on ₹20,000 at 16% p.a. for 9 months compounded quarterly.
Solution:
Compounded quarterly means 4 times a year.
P = ₹20,000
Annual Rate = 16%, so Quarterly Rate = 16%/4 = 4% per quarter
Time = 9 months = 9/3 = 3 quarters
A = P (1 + R/100)^T
= 20000 × (1 + 4/100)³
= 20000 × (1.04)³
= 20000 × 1.124864
= ₹22,497.28
CI = A – P
= 22497.28 – 20000
= ₹2,497.28
Answer: ₹2,497.28
10. Find the amount and CI on ₹24,000 compounded semi-annually for 1 ½ years at the rate of 10%.
Solution:
P = ₹24,000
Annual Rate = 10%, so Semi-annual Rate = 10%/2 = 5% per half-year
Time = 1.5 years = 3 half-years
A = P (1 + R/100)^T
= 24000 × (1 + 5/100)³
= 24000 × (1.05)³
= 24000 × 1.157625
= ₹27,783
CI = A – P
= 27783 – 24000
= ₹3,783
Answer: Amount = ₹27,783, CI = ₹3,783
11. Find the amount and compound interest on ₹1,00,000 compounded semi-annually for 1 ½ years at the rate of 8% p.a.
Solution:
P = ₹1,00,000
Annual Rate = 8%, so Semi-annual Rate = 8%/2 = 4% per half-year
Time = 1.5 years = 3 half-years
A = 100000 × (1 + 4/100)³
= 100000 × (1.04)³
= 100000 × 1.124864
= ₹1,12,486.40
CI = A – P
= 112486.40 – 100000
= ₹12,486.40
Answer: Amount = ₹1,12,486.40, CI = ₹12,486.40
12. Find the compound interest and amount on ₹35,000 for 1 ½ years compounded semi-annually at the rate of 12% p.a.
Solution:
P = ₹35,000
Annual Rate = 12%, so Semi-annual Rate = 12%/2 = 6% per half-year
Time = 1.5 years = 3 half-years
A = 35000 × (1 + 6/100)³
= 35000 × (1.06)³
= 35000 × 1.191016
= ₹41,685.56
CI = A – P
= 41685.56 – 35000
= ₹6,685.56
13. Application-Based Question: Seema invested ₹6400 for 3 years at the rate of 10% per annum compounded annually. Somalia saw the same amount at the same rate for the same time but on simple interest. Who gets more interest by how much?
Solution:
Calculate Seema’s Compound Interest (CI)
P = ₹6400, R = 10%, T = 3 years
A = 6400 × (1 + 10/100)³
= 6400 × (1.10)³
= 6400 × 1.331
= ₹8,518.40
CI = A – P = 8518.40 – 6400 = ₹2,118.40
Calculate Somalia’s Simple Interest (SI)
SI = (P × R × T) / 100
= (6400 × 10 × 3) / 100
= ₹1,920
: Compare
Seema gets more interest.
Difference = CI – SI = 2118.40 – 1920 = ₹198.40
Answer: Seema gets more interest, by ₹198.40.