Simple Interest and Compound Interest Question 2 - CAT 2021
Bank A offers a 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:
Step-by-Step Explanation
- Analyze Bank A (Effective Compound Interest Rate):
Bank A offers a 6% nominal annual rate compounded half-yearly.
○ Half-yearly rate = 6% / 2 = 3%
○ Effective annual interest rate factor = (1 + 0.03)² − 1 = 1.0609 − 1 = 0.0609 (or 6.09%)
- Analyze Raju's Investment (Bank B):
Let Raju's principal be P, the simple interest rate of Bank B be x% per annum, and the time period be t years.
Raju's Interest = P × x × t / 100
We are told this equals the interest earned if P was put into Bank A for one year:
P × x × t / 100 = P × 0.0609 ⇒ xt / 100 = 0.0609
- Analyze Rupa's Investment (Bank C):
○ Principal = ₹ 10,000
○ Rate = 2x% (twice Bank B's rate)
○ Time = 2t (twice Raju's investment period)
Set up the simple interest formula for Rupa:
Rupa's Interest = (10,000 × 2x × 2t)/ 100
Rupa's Interest = 40,000 × (xt / 100)
- Substitute the known value:
Substitute xt / 100 = 0.0609 into Rupa's equation:
Rupa's Interest = 40,000 × 0.0609 = 2436
The interest accrued to Rupa is ₹ 2436.
Correct Option: B
💡 FundaMakers Tip:
When a problem leaves individual variables like x and t unsolvable on their own, don't panic! Look at them as a unified compound block (xt).
Notice the internal structural scaling: doubling the rate (× 2) and doubling the time (× 2) means the interest multiplier block increases by a factor of 2 × 2 = 4.
Rupa's interest is simply: 4 × (Effective Rate of A) × (Rupa's Principal).
4 × 0.0609 × 10,000 = 2436
Spotting this scaling factor completely eliminates the need to worry about Raju's missing principal or specific timelines.