Question

Mr. Verma invested Rs. 90,000 in a mutual fund which increased by a% the first year. He withdrew the extra amount after a year. From then onwards, he received compound interest of 3a% which is compounded once every 4 months. But the income tax department charged 30% on the interest which exceeds 20% of the initial investment. Find the amount withdrawn by him after one year if he pays Rs. 14256 as tax.

• A. Rs. 9,000
• B. Rs. 13,500
• C. Rs. 18,000
• D. Rs. 27,000
• E. Rs. 24,000

Answer 1

The Correct Option is C

Total taxable amount 

= \(14256 \times \frac{100}{30}\) = Rs. \(47520\)

Also, \(20\%\) of \(90,000 = 18,000\) is exempted from the tax.

So, total interest = \(47520 + 18,000 = 65,520\)

As interest is compounded every \(4\) months, rate of interest = \(\frac{3a\%}{3}\)  = \(a\%\) and time period = \(1\times3 = 3\).

So, amount = \(90,000 + 65,520 = 90,000(1+\frac{3a}{3\times100})^3\)

\(1,55,520 = 90,000(1+a\%)^3\)

\((1+a\%)^3 = \frac{1,55,520}{90,000} = \frac{1728}{1000} = \bigg(\frac{12}{10}\bigg)^3\)

\(1+a\% = \frac{12}{10}\)

or, \(a\% = 20\%\)

The amount withdrawn by him after one year = \(\frac{20}{100} \times 90,000 = 18,000\)

Hence, option C is the correct answer.