Sahil received ₹10,000 as a prize in a poster-making competition. His father promises to pay him 12 per cent interest per year if he does not spend the amount. After 3 years, how much money would Sahil have?
This question applies the concept of compound interest. The chapter demonstrates how interest is earned not just on the original amount but also on previously earned interest.
Step 1: Calculate the amount after Year 1
- Principal = ₹10,000
- Interest for Year 1 = 12% of ₹10,000 = (12/100) × 10,000 = ₹1,200
- Amount after Year 1 = ₹10,000 + ₹1,200 = ₹11,200
Step 2: Calculate the amount after Year 2
- Principal for Year 2 = ₹11,200
- Interest for Year 2 = 12% of ₹11,200 = (12/100) × 11,200 = ₹1,344
- Amount after Year 2 = ₹11,200 + ₹1,344 = ₹12,544
Step 3: Calculate the amount after Year 3
- Principal for Year 3 = ₹12,544
- Interest for Year 3 = 12% of ₹12,544 = (12/100) × 12,544 = ₹1,505.28
- Amount after Year 3 = ₹12,544 + ₹1,505.28 = ₹14,049.28
Final Answer: Sahil would have ₹14,049.28 after 3 years.
Explanation
This question applies the concept of compound interest explained in the chapter. The chapter demonstrates how interest is earned not just on the original amount but also on previously earned interest. Using the same method shown in the chapter's example of ₹1000 at 6% interest, we calculate compound interest for Sahil's ₹10,000 at 12% interest for 3 years.
Solution Steps
Step 1: Calculate the amount after Year 1
Principal = ₹10,000
Interest for Year 1 = 12% of ₹10,000 = (12/100) × 10,000 = ₹1,200
Amount after Year 1 = ₹10,000 + ₹1,200 = ₹11,200
Step 2: Calculate the amount after Year 2
Principal for Year 2 = ₹11,200
Interest for Year 2 = 12% of ₹11,200 = (12/100) × 11,200 = ₹1,344
Amount after Year 2 = ₹11,200 + ₹1,344 = ₹12,544
Step 3: Calculate the amount after Year 3
Principal for Year 3 = ₹12,544
Interest for Year 3 = 12% of ₹12,544 = (12/100) × 12,544 = ₹1,505.28
Amount after Year 3 = ₹12,544 + ₹1,505.28 = ₹14,049.28
Final Answer: Sahil would have ₹14,049.28 after 3 years.