Question

In how many years will 750 rupees, amount to 900 rupees at 7% per annum.

Answer 1

Hint: Simple interest or interest figured on the principal amount only, for the duration of the loan.
The rate % (percentage) per annum on the principal amount and the duration of the loan are the factors for calculating simple interest.
The total amount received at the end of duration of loan is the sum of principal amount and interest.
When numbers of years are converted into days, it is always multiplied by 365, whether it is a leap year or an ordinary year.

Complete step by step solution:
Step 1: State the given information and assume unknowns
Let the time = t years
Principle amount, P = 750 rupees
Total amount, A = 900 rupees

Step 2:
We know, the total amount received at the end of duration of loan is the sum of principal amount and interest.
Thus, A = P + I
Here, A = total amount
           P = principle amount
           I = simple interest
Hence, Interest, I = total amount – principal amount
                             I = A – P
                             = 900 - 750
                             I = 150
Step 3: Here, I, P and r are known, only one term is unknown time period, t
Therefore,
 Using Simple interest formula:
           ${\rm{I}} = \dfrac{{\Pr t}}{{100}}$
$ \Rightarrow 150 = \dfrac{{750 \times 7 \times t}}{{100}}$
$\begin{array}{l}
 \Rightarrow {\rm{ }}t = \dfrac{{100 \times 150}}{{750 \times 7}}\\
 \Rightarrow {\rm{ }}t = \dfrac{{100 \times 15{0}}}{{75{0} \times 7}}
\end{array}$
$ \Rightarrow {\rm{ }}t = \dfrac{{20}}{7}$ years
Or t = 2.85 years.
Step 4: Convert the fraction years of time period into days.
1 year = 365 days.
\[\begin{array}{l}
0.85{\rm{ years}} = 0.85 \times 365{\rm{ days}}\\
{\rm{ }} = 310.25{\rm{ days}}\\
{\rm{ }} \simeq 311{\rm{ days}}
\end{array}\]
Therefore, t = 2 years and 311 days.

Therefore, In 2 years 311 the 750 rupees will amount to 900 rupees at 7% per annum.

Note:
Day on which the money is borrowed is not counted but the day on which the money is returned is counted.
Simple interest or interest figured on the principal amount only, for the duration of the loan.