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
- 2436
- 3436
- 2346
- 1436
The Correct Option is A
Approach Solution - 1
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 is:
\[ A = P\left(1 + \frac{r}{2}\right)^2 \] where \( r \) is the rate of interest in decimal form.
Amount after 1 year = \( P \times \left(1 + 0.03\right)^2 = P \times \left(1.03\right)^2 = 1.0609P \)
Interest from Bank A for 1 year is:
\[ \text{Interest} = 1.0609P - P = 0.0609P \]
2) Interest earned by Raju from Bank B for time \( t \):
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 \( R \). The interest is:
\[ \text{Interest} = P \times R \times t = 0.0609P \] Thus, we have the equation: \[ R \times t = 0.0609 \]
3) Bank C's interest rate is \( wR \):
The interest Rupa earns from Bank C is:
\[ \text{Interest} = 10000 \times wR \times 2t = 20000 \times wR \times t \] From step 2, we know \( wR \times t = 0.0609 \), so we can substitute it into the equation:
\[ \text{Interest} = 20000 \times 0.0609 = ₹1218 \]
Since Rupa invests for \( 2t \) time, the total interest earned is:
\[ 2 \times ₹1218 = ₹2436 \]
Conclusion: The correct answer is ₹2436.
Approach Solution -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. After a year of investment in Bank A by Principal \( P \), the amount becomes:
\(P(1.03)(1.03) = P(1.0609)\) at the end of the year.
This means that the interest rate is 6.09% annually when looking at it as a simple interest plan.
Rupa's Investment in Bank C:
Rupa invests in Bank C, which offers twice the interest rate as Bank B and twice the investment amount. As a result, Rupa essentially receives four times the interest that Raju receives from making the identical investment in Bank A.
Assume Raju made a ₹10,000 investment in Bank B. Since this is equivalent to making a one-year investment in Bank A, the interest Raju will receive from his ₹10,000 investment is 6.09% of ₹10,000, which amounts to ₹609.
Rupa now needs to make four times as much as ₹609 for the same investment. Therefore, the interest Rupa earns is:
\(₹ 609 \times 4 = ₹ 2,436\)
Conclusion: Rupa earns ₹ 2,436 as interest from her investment in Bank C.
Top Questions on Interest
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Statement I: Relation between the nominal rate and effective rate : ref= (1 + 2) * r k +1, where ref = effective rate of interest r = nominal rate of interest k = numbers of conversion periods per year
Statement II: The nominal interest rate is also known as force of interest.
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