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Q.

Find the approximate rate of compound interest at which Rs. 1000 becomes Rs. 5000 in 4 years.

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a

10%

b

15%

c

50%

d

30%

answer is C.

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Detailed Solution

Let us first understand the formula for the amount after applying compound interest to it.
The formula for final amount is given by the following expression:-

\Rightarrow A = P {(1 + \frac{R}{100})}^{n}

, where A is the final amount, P is the Principal amount, R is the rate of compound interest and n is the amount of time ( in years ).
Now, since, we are given that P = 1000, A = 5000 and n = 4.
Putting all of these in the above expression, we will then obtain the following expression:-

\Rightarrow 5000 = 1000 {(1 + \frac{R}{100})}^{4}

Now, we will take the 1000 from multiplication in RHS to division in LHS to obtain the following expression:-

\Rightarrow \frac{5000}{1000} = {(1 + \frac{R}{100})}^{4}

Simplifying the LHS of the above expression to get the following new expression:-

\Rightarrow 5 = {(1 + \frac{R}{100})}^{4}

Now, we will take the power of

\frac{1}{4}

on both sides of the above expression. We will then obtain:-

\Rightarrow {(5)}^{\frac{1}{4}} = {[{(1 + \frac{R}{100})}^{4}]}^{\frac{1}{4}}

Now, since we know that (xa)1a=x. Using this in the RHS of above expression, we will obtain as follows:-

\Rightarrow 5^{\frac{1}{4}} = 1 + \frac{R}{100}

Now, putting the value of

5^{\frac{1}{4}} as 1.495

in above expression to get:-

\Rightarrow 1.495 = 1 + \frac{R}{100}

Now taking the 1 from addition in RHS to subtraction in LHS, we will obtain as follows:-

\Rightarrow 1.495 - 1 = \frac{R}{100}

Simplifying the LHS to get:-

\Rightarrow 0.495 = \frac{R}{100}

Taking 100 from division in RHS to multiplication in LHS, we will get:-
⇒R = 49.5
This is very near to 50.
∴ The correct option (3) is 50%.

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