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

The Correct Option is A

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.

Answer 2

Bank A offers a six percent interest rate that compounds every six months. 
This equates to a half-year interest rate of three percent.
Thus, after a year of investment in bank A by Principal P, it becomes 
\(P(1.03)(1.03) = P(1.0609)\) at the end of the year. 

As a result, the interest rate is 6.09% annually when looking at it as a simple interest plan. 
As a result of Rupa's investment in Bank C, which has twice the interest rate as Bank B and twice the investment amount, she essentially receives four times the interest that Raju receives for making the identical investment in Bank A. 
Assume Raju made a ₹10,000 investment in Bank B. 
Given that this is equivalent to making a one-year investment in Bank A, his interest will be 6.09% of 10,000, or ₹ 609. 
Rupa now needs to make four times as much as ₹ 609 for the same investment. 
Rupa therefore makes ₹ 2,436.