Question

In how many years will \[1000\] amount to \[1400\] at the rate of \[4\% \] per annum simple interest?

Answer 1

Hint: Here, we will subtract the principal from the amount to get the simple interest. We will then substitute the value of principal, rate of interest and simple interest in the simple interest formula to find the required number of years.

Formula used:
 We will use the following formula:
1.Simple Interest is given by \[S.I. = A - P\] where \[A\] is the amount, \[P\] is the principal, \[S.I\] is the Simple Interest.
2.Simple Interest is given by the formula \[S.I. = \dfrac{{P \times n \times r}}{{100}}\] where \[S.I\] is the Simple Interest, \[P\] is the principal, \[r\] is the rate of Interest and \[n\] is the number of years.

Complete step-by-step answer:
We are given that the principal is \[{\rm{Rs}}.1000\], the amount is \[{\rm{Rs}}.1400\] and the rate of interest is \[4\% \] per annum.
Now, we will find the Simple Interest in terms of Amount and Principal.
By substituting 1000 for the Principal and 1400 for the Amount in the formula \[S.I. = A - P\], we get
\[S.I. = 1400 - 1000\]
Subtracting the terms, we get
\[ \Rightarrow S.I. = 400\]
Now, we will find the number of years using the simple interest.
Let \[n\] be the number of years.
By substituting 1000 for the Principal, 400 for the simple interest and 4 for the rate of interest in the formula \[S.I. = \dfrac{{P \times n \times r}}{{100}}\], we get
\[400 = \dfrac{{1000 \times n \times 4}}{{100}}\]
Dividing the numerator by 100, we get
\[ \Rightarrow 400 = 10 \times n \times 4\]
Multiplying the terms, we get
\[ \Rightarrow 400 = 40 \times n\]
Dividing both sides by 40, we get
\[ \Rightarrow n = \dfrac{{400}}{{40}}\]
\[ \Rightarrow n = 10\]
Therefore, the number of years is \[10\] to obtain an amount of \[{\rm{Rs}}.1400\] from the principal of \[{\rm{Rs}}.1000\] at rate of \[4\% \] per annum.

Note: Here, we should not get confused between the simple interest and compound interest. The main difference between simple interest and compound interest is that simple interest is based only on the principal amount whereas compound interest is based on the principal amount and also the interest compounded for a period. We should remember that in simple interest the interest and the principal has to be added to find the amount. However, in compound interest, the amount obtained after adding the principal and interest for first year becomes principal for second year.