Question

How do you calculate interest paid daily ?

Answer 1

Hint: First we will let an imaginary amount and rate of interest and the time to calculate the simple interest of the considered amount and then using the relation of the number of days in a year , we will calculate the amount of interest in a day by dividing the simple interest by \[365\] for one year of time .

Complete answer: Given :

Let us consider that the values for the principal amount , rate of interest and time period is given as :

\[Principal{\text{ }}amount = Rs{\text{ }}5000\]
\[Rate{\text{ }}of{\text{ }}interest = 6\dfrac{1}{4}\% {\text{ }}per{\text{ }}annum\]
\[Time = 2years\]

We also know that the formula for simple interest is stated as :
\[S.I. = \dfrac{{P \times R \times T}}{{100}}\]
Where \[P\] is the principal amount , \[R\] is the rate of interest per annum and \[T\] is the time in years .

Putting the values , we get the simple interest of the considered amount as :
\[S.I. = \dfrac{{5000 \times 6\dfrac{1}{4} \times 2}}{{100}}\]

On simplifying , we get
\[S.I. = \dfrac{{5000 \times 6.25 \times 2}}{{100}}\]
\[S.I. = Rs625\]

[This is the simple interest for the time period of \[2\] years]

Now , as we know that the relation between the days and year is given as :
\[1{\text{ }}year = 365{\text{ }}days\]

Now , the simple interest is for \[2\] years so the number of days in \[2\] years is given as :
\[2{\text{ }}years = 2 \times 365\]
\[2{\text{ }}years = 730days\]

Now , we can calculate the simple interest per day as :
\[Daily{\text{ }}Interest = \dfrac{{S.I.}}{{number{\text{ }}of{\text{ }}days}}\]

Putting the values , we get
\[Daily{\text{ }}Interest = \dfrac{{625}}{{730}}\]

On solving , we get the interest daily as :
\[Daily{\text{ }}Interest = Rs{\text{ }}0.86\]

Hence , we conclude that for the considered value the interest paid daily is \[Rs{\text{ }}0.86\] .

Note:
We wrote the value of rate of interest of amount \[6\dfrac{1}{4}\] as \[6.25\] . As using the property of writing the percentage of fixed fraction into its real number form .
The mixed fraction can be written as :
\[6\dfrac{1}{4} = \dfrac{{6 \times 4 + 1}}{4}\]
\[6\dfrac{1}{4} = \dfrac{{25}}{4}\]
And on solving , we get
\[6\dfrac{1}{4} = 6.25\]