Question

Kruti took a loan at simple interest 6 percent in the first year with an increment of 0.5% in each subsequent year. She paid Rs 3375 as interest after 4 years. How much loan did she take?
$\begin{align}
  & \text{a) Rs12500} \\
 & \text{b) Rs15800} \\
 & \text{c) Rs33250} \\
 & \text{d) Rs30000} \\
\end{align}$

Answer 1

Hint: Now we know that the formula for simple interest is $\dfrac{\text{amount }\!\!\times\!\!\text{ (percent of interest) }\!\!\times\!\!\text{ time}}{100}$
Since we are given the percent of interest for each year we can calculate the simple interest of every year. Then the total interest is sum of interest of each year

Complete step by step answer:
Now let the loan taken be x Rs. Then we know that the formula for interest is $\dfrac{\text{amount }\!\!\times\!\!\text{ (percent of interest) }\!\!\times\!\!\text{ time}}{100}$
Now for first year the rate of interest is 6 percent
Hence we have interest for first year is $\dfrac{x\times 6\times 1}{100}=\dfrac{6x}{100}.................(1)$
Now the interest percent increases by 0.5 percent each year
Hence for 2nd year interest percent is 6.5 percent, Now we get interest as
$=\dfrac{x\times 6.5\times 1}{100}=\dfrac{6.5x}{100}................(2)$
Now since the interest percent increases by 0.5 percent each year
Hence for 3rd year interest percent is 7 percent, Now we get interest as
$=\dfrac{x\times 7\times 1}{100}=\dfrac{7x}{100}................(3)$
Now since the interest percent increases by 0.5 percent each year
Hence for 4th year interest percent is 7.5 percent, Now we get interest as
$=\dfrac{x\times 7.5\times 1}{100}=\dfrac{7.5x}{100}................(4)$
Hence from equation (1), equation (2), equation (3) and equation (4) we get the total interest is
$\begin{align}
  & =\dfrac{6x}{100}+\dfrac{6.5x}{100}+\dfrac{7x}{100}+\dfrac{7.5x}{100} \\
 & =\dfrac{6x+6.5x+7x+7.5x}{100} \\
 & =\dfrac{(6+6.5+7+7.5)x}{100} \\
 & =\dfrac{27x}{100} \\
\end{align}$
Now we are given that the total interest is 3375 Rs.
Hence we get,
$\begin{align}
  & \dfrac{27x}{100}=3375 \\
 & \Rightarrow x=\dfrac{3375\times 100}{27}=125\times 100=12500 \\
\end{align}$
Hence we get that x = 12500.
Hence Kriti took a loan of 12500.

Note:
Note that the formula for simple interest is $\dfrac{\text{amount }\!\!\times\!\!\text{ (percent of interest) }\!\!\times\!\!\text{ time}}{100}$ and the formula for compound interest compounded annually is $P{{\left( 1+i \right)}^{t}}-P$ . Hence not to be confused among the two as the variables in both are the same. Also note that the period of loan is different, for both the amounts and therefore the interest accumulated on them would be different.