1️⃣ What is the compound interest on ₹100 for 1 year at 10% per annum, compounded annually?
Step-by-Step Explanation
Amount (A) = P(1 + R/100)^T.
A = 100(1 + 10/100)^1.
A = 100(1.1)^1.
A = 110.
Compound Interest (CI) = A - P.
CI = 110 - 100 = ₹10.
Answer: ₹10 ✅
2️⃣ What is the compound interest on ₹200 for 2 years at 5% per annum, compounded annually?
Step-by-Step Explanation
A = P(1 + R/100)^T.
A = 200(1 + 5/100)^2.
A = 200(1.05)^2.
A = 200(1.1025).
A = 220.50.
CI = A - P.
CI = 220.50 - 200 = ₹20.50.
Answer: ₹20.50 ✅
3️⃣ Find the compound interest on ₹1000 at 10% per annum for 1.5 years, compounded annually.
Step-by-Step Explanation
For the first year:
A1 = 1000(1 + 10/100)^1.
A1 = 1000(1.1) = 1100.
For the next 6 months (0.5 years):
SI = (1100 * 10 * 0.5) / 100.
SI = 55.
Total amount = 1100 + 55 = 1155.
CI = 1155 - 1000 = ₹155.
Answer: ₹155 ✅
4️⃣ If the compound interest on a sum for 2 years at 10% per annum is ₹210, find the principal amount.
Step-by-Step Explanation
Let the principal be P.
A = P(1 + 10/100)^2.
A = P(1.1)^2.
A = 1.21P.
CI = A - P.
210 = 1.21P - P.
210 = 0.21P.
P = 210 / 0.21.
P = ₹1000.
Answer: ₹1000 ✅
5️⃣ A sum of money becomes 9 times itself in 2 years at compound interest. What is the rate of interest per annum?
Step-by-Step Explanation
Let the principal be P.
Amount = 9P.
A = P(1 + R/100)^2.
9P = P(1 + R/100)^2.
9 = (1 + R/100)^2.
3 = 1 + R/100.
2 = R/100.
R = 200%.
Answer: 200% ✅
6️⃣ A certain sum of money amounts to ₹1008 in 2 years and to ₹1164 in 3.5 years. Find the rate of interest per annum.
Step-by-Step Explanation
SI for 1.5 years = 1164 - 1008 = ₹156.
SI for 1 year = 156 / 1.5 = ₹104.
SI for 2 years = 104 * 2 = ₹208.
Principal (P) = 1008 - 208 = ₹800.
SI = (P * R * T) / 100.
104 = (800 * R * 1) / 100.
104 = 8R.
R = 104 / 8.
R = 13%.
Answer: 13% ✅
7️⃣ A sum of money is lent at simple interest at a certain rate for 3 years. Had it been lent at 2% higher rate, it would have fetched ₹360 more. Find the sum of money.
Step-by-Step Explanation
Let the principal (P) be x.
Difference in SI = (P * 2 * 3) / 100.
360 = 6P / 100.
36000 = 6P.
P = 36000 / 6.
P = ₹6000.
Answer: ₹6000 ✅
8️⃣ A person lent out a certain sum on simple interest and after 4 years he received a sum which was 5/4 times the original sum. Find the rate of interest.
Step-by-Step Explanation
Let the principal (P) be x.
Amount (A) = (5/4)x.
SI = A - P = (5/4)x - x = (1/4)x.
SI = (P * R * T) / 100.
(1/4)x = (x * R * 4) / 100.
100x = 16xR.
R = 100 / 16 = 6.25%.
Answer: 6.25% ✅
9️⃣ A sum of money amounts to ₹14,580 in 2 years and ₹17,496 in 3 years at compound interest. Find the rate of interest per annum.
Step-by-Step Explanation
Let P be the principal and R be the rate of interest.
Amount after 2 years: P(1 + R/100)^2 = 14580.
Amount after 3 years: P(1 + R/100)^3 = 17496.
Dividing the second equation by the first: (1 + R/100) = 17496 / 14580 = 1.2.
R/100 = 1.2 - 1 = 0.2.
R = 0.2 × 100 = 20%.
Answer: 20% ✅
🔟 A sum of money, when invested at compound interest, grows to 2.25 times its original value in 2 years. What is the annual rate of interest?