Compound Interest questions test your ability to apply percentage values and exponents. But, they also test your ability to apply logic in inferring certain hidden clues.
This question is actually easy because, interest is compounded annually on the amounts deposited at both the banks. Had one of them been calculated annually and the other half-yearly/quarterly/monthly, this question would have become much more difficult to tackle.
In questions on CI, taking a slightly larger number is advisable because it reduces the possibility of having to deal with vulgar fractions. In this question,
let’s assume that
$1000 was deposited at bank A and
$500 was deposited at bank B. Bank A offers x% interest which is compounded annually, while B offers y% interest which is compounded annually as well.
At this stage, you need to ask yourself this question –>
if x = y, where will I get a higher total interest? Your answer to this question would be
‘from bank A’. That’s because the amount that you have invested in A is so much larger (double) than the one you have invested in B that, if the interest rates were same, then, naturally bank A would give you more total interest.
This is when you understand that your answer depends more on knowing what the interest rates are than knowing what was the investment. This should naturally point you in the direction of statement I, but, let’s analyse it and see what it gives us.
Statement I alone says that y = 0.8x or y = (\(\frac{4}{5}\)) x.
Let’s assume the principal invested in bank A as 2P and that in bank B as P. Then,
Amount from bank A = \(2P (1+ \frac{x}{100})^3\) and
Amount from bank B = \(P (1+ \frac{4x}{500})^3\) = \(P(1+\frac{x}{125})^3\).
Clearly, in the second case, the term inside the bracket will be much smaller than the one in the first case. And when you raise it to an integral power, you’ll obtain a smaller value in the second case as compared to the first case.
We can infer that the person obtained a higher total profit from bank A than from bank B.
An alternative approach (and one that’s close to my heart) in analyzing statement I would be to
take simple values for the variables and evaluate. I’d pick the
investment in A as $1000 and in B as $500. I’d pick
x = 10% pa and consequently
y = 8% pa. Applying these values, we get,
Amount from bank A = 1000 \((1.1)^3\) = 1000 * 1.331 = 1331 and
Amount from bank B = 1000 \((1.08)^3\) = 1000 * 1.26 (approximately) = 1260.
Statement I alone is sufficient. Possible answer options are A or D. Answer options B, C and E can be eliminated.
From statement II alone, we can understand that the investments in bank A and bank B are $200 and $100 respectively. However, since the values of x and y can be anything, we cannot conclusively say about which bank will give us a higher interest.
If x is more than y, bank A is naturally going to give you more than bank B.
But, if x is infinitely small when compared to y, bank B can still give more than bank A.
Statement II alone is insufficient, answer option D can be eliminated.
The correct answer option is A.
Hope that helps!
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