Question
Download Solution PDFA sum of money becomes 3/5 times more in 6 years at simple interest. What will be the compound interest of Rs 12000 after 3 years at the same rate?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
In 6 years, amount becomes 3/5 times more ⇒ Interest = 3/5 of principal
Let principal = P ⇒ SI = (3/5)P
Time = 6 years
We need to find CI on ₹12,000 for 3 years at same rate
Formula used:
Simple Interest: SI = (P × R × T) ÷ 100
Compound Interest: A = P\((1 + \frac{r}{100})^t\)
CI = A - P
Calculations:
SI = (3/5)P = (P × R × 6) ÷ 100
⇒ (3/5)P = (6PR) ÷ 100
⇒ Multiply both sides by 100: 60P = 6PR ⇒ R = 10%
Now for CI on ₹12,000 for 3 years at 10%:
A = 12000 × (1 + 10/100)3 = 12000 × (1.1)3 = 12000 × 1.331 = ₹15,972
CI = 15972 - 12000 = ₹3,972
∴ Compound Interest = ₹3,972
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