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

• A. 2436
• B. 3436
• C. 2346
• D. 1436

Answer 1

Answer: (A)

2436

Answer 2

Let's solve the problem step by step:

Given:
For Bank A: 6% interest p.a compounded half-yearly, which means interest is 3% for every half year. For Bank C: The annual interest rate is w times that of Bank B.
Raju invests P in Bank B for t time period and Rupa invests ₹10,000 in Bank C for 2t time period.
The interest that Raju earns from Bank B in t time = Interest from Bank A in 1 year.

1. Calculating interest for Bank A:
   For compounded half-yearly, the amount after 1 year = $P(1 +\frac{ r}{2})^2$,
   where r is the rate of interest in decimal form.
   Amount after 1 year = $P(1 + 0.03)^2 = P(1.03)^2 = 1.0609P$
   Interest from Bank A for 1 year =$1.0609P - P = 0.0609P$

2. Given that the interest Raju earns from Bank B for t time = 0.0609P (from the above calculation).
   Let the interest rate of Bank B be R. Interest = $P \times R \times t = 0.0609P$
   $⇒ R \times t = 0.0609$

3. Bank C interest rate = wR
   Interest Rupa earns from Bank C = $10000 \times wR \times 2t$
   $= 20000 \times wR \times t$

Given,$wR \times t = 0.0609$ (from the 2nd step)
$⇒ wR \times t =\frac{ 0.0609 \times P}{P}$ (where P cancels out)
$⇒ wR = \frac{0.0609}{t}$

The interest Rupa earns = $20000 \times 0.0609$
= ₹1218

But this is only for t time period. Rupa invests for 2t, so the total interest is $2 \times ₹1218 = ₹2436.$
So, the correct answer is ₹2436.