Question

\[14000\] is invested at \[4\% \] per annum simple interest. How long will it take for the amount to reach 16240?

Answer 1

Hint: Firstly we find out the value of the simple interest. To find the difference between the simple interest and the compound interest ,first calculate the simple interest by subtracting principal money from the total money.

Formula used: Use the concept of the simple interest
\[S.I. = \dfrac{{P \times R \times T}}{{100}}\]
Where \[I = \]interest earned after \[t\] year
\[P = \]money borrowed or invested
\[R = \]annual rate of interest
\[T = \]the length of time you borrow or invest

Complete step-by-step solution:
Given the value of the rate of the interest\[ = 4\% \]
Principal\[ = \]Rs\[14000\]
Total amount\[ = 16240\]
We know that simple interest\[ = \]total amount\[ - \]principal amount……………..\[1\]
Substitute the value of the total amount and principal amount in equation \[1\] we get
S.I.\[ = A - P\]
Substituting the value of A and P we get,
S.I \[ = \].\[16240 - 14000\]
So simple interest ,
S.I.\[ = 2240\]
Use the concept of the simple interest
\[S.I. = P \times R \times T\]
Then \[T = \dfrac{{S.I. \times 100}}{{P \times R}}\].......................\[2\]
Substitute the value of the \[S.I.,P\] and \[R\] in the equation \[2\] we get
\[T = \dfrac{{100 \times 2240}}{{14000 \times 4}}\]
Rewrite the equation after simplification we get
\[T = \dfrac{{224000}}{{56000}}\]
\[224000\] is divided by the \[56000\] we get
\[T = 4\]

Hence the value of the length of the time is \[4\] years

Note: In the calculation of the compound interest if we take small compounding time then the compound interest will be high as the compounding time will increase the amount of the compound interest will decrease. Compound interest is always higher than the simple interest for the same time period and same rate of interest only expect the first year. In first year CI and SI are the same.