Question

Rita borrowed $\$1600$ at $12\%$ interest for 90 days. How much interest did she pay on the loan?
(a) $\$1640$
(b) $\$48$
(c) $\$192$
(d) $\$80$

Answer 1

Hint: In the above question, principal is given as $\$1600$, rate of interest is given as $12\%$ p.a. and time on which interest has been applied is 90 days. To find the interest we are going to use the formula for simple interest (S.I.) which is given as $S.I.=\dfrac{P\times R\times T}{100}$ where “P” represents principal, “R” represents rate of interest and “T” represents time (in years)

Complete step by step solution:
It is given that principal is equal to $\$1600$, rate of interest is given as $12\%$ p.a. and time on which interest has been applied is equal to 90 days.
We are asked to find the simple interest which we will find by using the formula of simple interest.
The formula of simple interest is equal to:
$S.I.=\dfrac{P\times R\times T}{100}$…………… Eq. (1)
In the above equation, “P” stands for principal, “R” stands for rate of interest and “T” represents the time period in years.
As the time given in the above problem is in days so we have to convert this time (in days) to years as follows:
We know that in 1 years, 365 days are there which we are shown as follows:
$\Rightarrow 1year=365days$
Then 1 day, the number of years is equal to:
$1day=\dfrac{1}{365}year$
Now, number of years can be calculated by multiplying 90 on both the sides of the above equation we get,
$\begin{align}
  & 1\times 90days=\dfrac{1}{365}\times 90year \\
 & \Rightarrow 90days=\dfrac{18}{73}year \\
\end{align}$
Substituting “P” as $\$1600$, rate of interest is given as $12\%$ p.a. and “T” as $\dfrac{18}{73}year$ in eq. (1) we get,
$S.I.=\dfrac{\left( 1600 \right)\times \left( 12 \right)\times \left( \dfrac{18}{73} \right)}{100}$
In the above equation, 100 will be cancelled out from the numerator and denominator of the right hand side of the above equation.
$\begin{align}
  & S.I.=\dfrac{\left( 16 \right)\times \left( 12 \right)\times \left( \dfrac{18}{73} \right)}{1} \\
 & \Rightarrow S.I.=\dfrac{3456}{73} \\
 & \Rightarrow S.I.=\$47.34\\\end{align}$
From the above, we have got the value of interest as $\$47.34$.

So, the correct answer is “Option b”.

Note: The mistake that could be possible in the above problem is that you may forget to convert days into years and then put the value of “T” in a simple interest formula so make sure you have converted the time given (either in days or months) to years first and then proceed.