What is the ratio of compound interest earned on a certain amount at the rate of 10% for 3rd year and 5th year?

Question of The Day30-11-2020

What is the ratio of compound interest earned on a certain amount at the rate of 10% for 3^rd year and 5^th year?

Answer

Correct Answer : c ) 100 : 121

Explanation :

According to the question:

Rate of interest = 10%

Time₁ = 3 years

Time₂ = 5 years

We know that,Compound interst CI=\({P[(1+{r\over100})^n}-1]\),

Here, P = principal amount, r = rate of interest and n = time

⇒CI of 3^rd year=\({P[(1+{10\over100})^3}-1]-{P[(1+{10\over100})^2}-1]\)

⇒CI of 3^rd year=\({P(1+{10\over100})^2}(1+{10\over100}-1)\)

⇒CI of 3^rd year=\({P(1+{1\over10})^2}({1\over10})\)

Similarly, CI of 5^th year =\({P(1+ {1\over10})^4}({1\over10})\)

Thus, the required ratio=\({P({11\over10})^2}({1\over10}) : {P({11\over10})^4}({1\over10}) \)

=10² :11²

= 100 : 121

Hence, (c) is the correct answer.

Such type of question is asked in various government exams like SSC CGL, SSC MTS, SSC CPO, SSC CHSL, RRB JE, RRB NTPC, RRB GROUP D, RRB OFFICER SCALE-I, IBPS PO, IBPS SO, RRB Office Assistant, IBPS Clerk, RBI Assistant, IBPS RRB OFFICER SCALE 2&3, UPSC CDS, UPSC NDA etc.

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