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Question:

Bank A offers 6% interest rate per annum compounded half yearly. Bank B and Bank C offer simple interest but the annual interest rate offered by Bank C is twice that of Bank B. Raju invests a certain amount in Bank B for a certain period and Rupa invests ₹ 10,000 in Bank C for twice that period. The interest that would accrue to Raju during that period is equal to the interest that would have accrued had he invested the same amount in Bank A for one year. The interest accrued, in INR, to Rupa is

Explanation:

Let Raju invests Rs. A in bank B at r% p.a. for t years.
∴ Rupa invests Rs. 10,000 in bank C at 2r% p.a. for 2t years.

Total interest accrued for Raju = Art/100

This is same as interest accrued by investing same amount in bank A for a year.

Amount due after 1 year in bank A = A ${[1 + \frac{3}{100}]}^{2}$ = 1.0609A
Interest accrued = 1.0609A - A = 0.0609A

⇒ 0.0609A = $\frac{A r t}{100}$

⇒ rt = 6.09

Now, interest accrued by Rupa = $\frac{10000 \times 2 r \times 2 t}{100}$ = 400 × rt = 400 × 6.09 = 2436.

Hence, option (d).

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