Answer
Hint: First, we will need to know about the concept of the compound interest. It can be calculated using the formula of compound interest = Amount – principal amount.
The amount formula is $A = P{(1 + \dfrac{R}{{100}})^T}$ where A is the amount, P is the principal amount, R is the rate of change per annum and T is the time taken.
Complete step by step answer:
Since from the given we have the amount as $Rs.5408$ and time taken as $2$ years and rate of change per annum
as $4\% $ per annum. Hence, we only need to calculate the principal amount.
Thus substitute all the know values into the given formula we have $A = P{(1 + \dfrac{R}{{100}})^T} \Rightarrow 5408 = P{(1 + \dfrac{4}{{100}})^2}$ where the amount is given as $A = 5408$ and the time taken is given as $T = 2$ and the rate of change per annum is given as $R = 4\% $
Thus, further solving we have $A = P{(1 + \dfrac{R}{{100}})^T} \Rightarrow 5408 = P{(1 + 0.04)^2}$ by a division operation
Now by
the addition operation, we get \[ \Rightarrow 5408 = P{(1.04)^2}\]
Now squaring the given number, we have \[ \Rightarrow 5408 = P \times 1.0816\]
Again, by division, we get $P = \dfrac{{5408}}{{1.0816}} \Rightarrow 5000$ and hence which is the principal amount.
Thus $Rs.5000$ sum will become $Rs.5408$ after $2$ years at $4\% $ per annum when the interest is compounded annually
Note:
Compound interest is the interest on the additional amount of the interest to the
principal amount sum.
Where the simple interest is the quick method of calculating the interests change on the given amount and then we can make use of the formula that $SI = \dfrac{{PRT}}{{100}}$ where the P is the principal amount given and R is the rate of change per annum and T is the time taken for the period.
- 2
- 3
- 1.5
- 5
Answer (Detailed Solution Below)
Option 1 : 2
Given:
Principal = Rs. 5000
Rate of Interest = 4%
CI = Rs. 408
Formula:
Amount = P(1 + R/100)n
Amount = P + Interest
Here, P = Principal, R = Rate, n = Time
Calculations:
Amount = 5000 + 408 = Rs. 5408
Let the time period = n years
⇒ 5000(1 + 4/100)n = 5408
⇒ (1 + 4/100)n = 5408/5000
⇒ (1 + 4/100)n = 2704/2500
⇒ (52/50)n = (52/50)2
⇒ n = 2 years
∴ Required time period is 2 years.
Let's discuss the concepts related to Interest and Compound Interest. Explore more from Quantitative Aptitude here. Learn now!
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Updated On: 27-06-2022
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