Exercise: 8-B
Q1: Find the amount and the compound interest on ₹5000 for 2 years at 8% per annum, compounded annually.
Step 1: Use the compound amount formula:
\[
A = P \left(1 + \frac{R}{100}\right)^T
\]
Where:
P = ₹5000, R = 8%, T = 2 years
Step 2: Substituting values:
\[
A = 5000 \left(1 + \frac{8}{100}\right)^2 = 5000 \left(1.08\right)^2 \\
A = 5000 \times 1.1664 = ₹5832
\]Step 3: Compound Interest = Amount − Principal
\[
CI = 5832 – 5000 = ₹832
\]Answer: Amount = ₹5832, Compound Interest = ₹832
Q2: Find the amount and the compound interest on ₹8000 for 2 years at 6% per annum, compounded annually.
Step 1: Use the compound amount formula:
\[
A = P \left(1 + \frac{R}{100}\right)^T
\]
Where:
P = ₹8000, R = 6%, T = 2 years
Step 2: Substituting the values:
\[
A = 8000 \left(1 + \frac{6}{100}\right)^2 = 8000 \left(1.06\right)^2 \\
A = 8000 \times 1.1236 = ₹8988.80
\]Step 3: Compound Interest = Amount − Principal
\[
CI = 8988.80 – 8000 = ₹988.80
\]Answer: Amount = ₹8988.80, Compound Interest = ₹988.80
Q3: Find the amount and the compound interest on ₹2500 for 2 years, compounded annually, the rate of interest being 6% during the first year and 8% during the second year.
Step 1: Principal for the first year = ₹2500
Rate for the first year = 6%
\[
\text{Amount after 1st year} = 2500 \left(1 + \frac{6}{100}\right) = 2500 \times 1.06 = ₹2650
\]Step 2: Now this ₹2650 becomes the principal for the second year
Rate for the second year = 8%
\[
\text{Amount after 2nd year} = 2650 \left(1 + \frac{8}{100}\right) = 2650 \times 1.08 = ₹2862
\]Step 3: Compound Interest = Final Amount − Original Principal
\[
CI = 2862 – 2500 = ₹362
\]Answer: Amount = ₹2862, Compound Interest = ₹362
Q4: Find the amount and the compound interest on ₹25000 for 3 years at 6% per annum, compounded annually.
Step 1: Use the compound amount formula:
\[
A = P \left(1 + \frac{R}{100}\right)^T
\]
Where:
P = ₹25000, R = 6%, T = 3 years
Step 2: Substituting the values:
\[
A = 25000 \left(1 + \frac{6}{100}\right)^3 = 25000 \left(1.06\right)^3 = 25000 \times 1.191016 = ₹29775.40
\]Step 3: Compound Interest = Amount − Principal
\[
CI = 29775.40 – 25000 = ₹4775.40
\]Answer: Amount = ₹29775.40, Compound Interest = ₹4775.40
Q5: Find the amount and the compound interest on ₹10000 for 3 years at 10% per annum, compounded annually.
Step 1: Use the compound amount formula:
\[
A = P \left(1 + \frac{R}{100}\right)^T
\]
Where:
P = ₹10000, R = 10%, T = 3 years
Step 2: Substitute the values:
\[
A = 10000 \left(1 + \frac{10}{100}\right)^3 = 10000 \times (1.10)^3 = 10000 \times 1.331 = ₹13310
\]Step 3: Compound Interest = Amount − Principal
\[
CI = 13310 – 10000 = ₹3310
\]Answer: Amount = ₹13310, Compound Interest = ₹3310
Q6: Karim took a loan of ₹25000 from Corporation Bank at 12% per annum, compounded annually. How much amount, he will have to pay at the end of 3 years?
Step 1: Use the compound amount formula:
\[
A = P \left(1 + \frac{R}{100}\right)^T
\]
Where:
P = ₹25000, R = 12%, T = 3 years
Step 2: Substitute the values:
\[
A = 25000 \left(1 + \frac{12}{100}\right)^3 = 25000 \times (1.12)^3 = 25000 \times 1.404928 = ₹35123.20
\]Answer: Karim will have to pay ₹35123.20 at the end of 3 years
Q7: Manoj deposited ₹15625 in a bank at 8% per annum, compounded annually. How much amount will he get after 3 years?
Step 1: Use the compound amount formula:
\[
A = P \left(1 + \frac{R}{100}\right)^T
\]
Where:
P = ₹15625, R = 8%, T = 3 years
Step 2: Substitute the values:
\[
A = 15625 \left(1 + \frac{8}{100}\right)^3 = 15625 \times (1.08)^3 = 15625 \times 1.259712 = ₹19683
\]Answer: Manoj will get ₹19683 after 3 years
Q8: A person lent out ₹16000 simple interest and the same sum on compound interest for 2 years at \(12\frac{1}{2}\)% per annum. Find the ratio of the amounts received by him as interests after 2 years.
Step 1: Given Principal = ₹16000
Rate = \(12\frac{1}{2} = \frac{25}{2}\)% per annum
Time = 2 years
Step 2: First, calculate Simple Interest:
\[
SI = \frac{P \times R \times T}{100} = \frac{16000 \times \frac{25}{2} \times 2}{100} \\
SI= \frac{16000 \times 25}{100} = ₹4000
\]Step 3: Now calculate Compound Interest:
\[
A = P \left(1 + \frac{R}{100} \right)^T = 16000 \left(1 + \frac{25}{200}\right)^2 = 16000 \left(1.125\right)^2 = 16000 \times 1.265625 = ₹20250 \\
CI = A – P = 20250 – 16000 = ₹4250
\]Step 4: Ratio of interests:
\[
SI : CI = 4000 : 4250 = \frac{4000}{250} : \frac{4250}{250} = 16 : 17
\]Answer: The required ratio is 16 : 17
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