Question : The Principal that yields a Compound Interest of Rs. 420 in the second year at 5% per annum is:
Option 1: Rs. 7,000
Option 2: Rs. 5,000
Option 3: Rs. 8,000
Option 4: Rs. 6,000
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Correct Answer: Rs. 8,000
Solution :
Let the Principal amount be Rs. $P$.
We know that Compound Interest amount $A=P(1+\frac{r}{100})^n$
The amount at the end of the first year $= P(1+\frac{5}{100})$
= $1.05P$
The amount at the end of the second year $= P(1+\frac{5}{100})^2$
= $1.1025P$
The Compound Interest earned in the second year is equal to the difference in the amount between the first and second years.
⇒ $1.1025P–1.05P=420$
⇒ $0.0525P = 8420$
⇒ $P$ = 8000
Hence, the correct answer is Rs. 8,000.
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