Question

A sum of money invested at 8% per annum for simple interest amounts to Rs.12122 in 2 years. What will it amount to in 2 years 8 months at 9% rate of interest?
A. 14050
B. 12958
C. 13256
D. 12220

Answer 1

Hint: The formula for amount of a simple interest is A = P(1 + r*t), where P is the initial principal balance, r is the simple interest rate per annum, t is the time (in years) and A is the final amount obtained on the principal balance. Put the values of A, r and t as given in the question and obtain the value of P. Using this value of P, with a different value of r and t, find the value of the final amount, as given in the question.

Complete step-by-step answer:
Let us assume the initial principal balance is Rs. P
Here, simple interest rate per annum is 8% , the time is 2 years and the final amount is Rs. 12122.

Putting the values A = 12122, r $=\text{ 8 }\!\!%\!\!\text{ = }\dfrac{8}{100}\text{ = 0}\text{.08}$ and t = 2 in the formula A = P(1 + r*t), we get,
$\begin{align}
  & 12122\text{ = P(1 + 0}\text{.08 * 2) } \\
 & \Rightarrow \text{ 12122 = P(1 + 0}\text{.16)} \\
 & \therefore \text{ P = }\dfrac{12122}{1.16} \\
 & \text{ = 10450} \\
\end{align}$
Thus, the initial principal balance in hand is Rs. 10,450.

Now, for the same principal balance, if the rate of simple interest and the time required are changed, then the final amount received will also change accordingly.
The new values are,
Annual rate of simple interest $=\text{ 9 }\!\!%\!\!\text{ = }\dfrac{9}{100}\text{ = 0}\text{.09}$
Time required
$\begin{align}
  & =\text{ 2 years 8 months} \\
 & \text{= 2 years + }\dfrac{8}{12}\text{ years} \\
 & \text{= 2}\dfrac{2}{3}\text{ years} \\
 & \text{= }\dfrac{8}{3}\text{ years} \\
\end{align}$

Hence, putting the values P = Rs.10,450, r = 0.09 and t $=\text{ }\dfrac{8}{3}$in the formula A = P(1 + r*t), we get,
$\begin{align}
  & \text{A = 10450(1 + }\dfrac{8}{3}\text{ x 0}\text{.09)} \\
 & \therefore \text{ A = 10450 x (1 + 0}\text{.24)} \\
 & \text{ = 10450 x 1}\text{.24} \\
 & \text{ = 12958} \\
\end{align}$
Thus, the final amount received is Rs. 12,958. Hence, the correct answer is option B.

Note: Alternatively, the problem can be solved without explicitly finding the principal balance. This can be done by putting the changed values of r and t in the formula A = P(1 + r*t), where P remains constant.
$\begin{align}
  & {{\text{A}}_{1}}\text{ = P}\left( \text{1 + }{{\text{r}}_{1}}*{{\text{t}}_{1}} \right)\text{ }....\text{(i)} \\
 & {{\text{A}}_{2}}\text{ = P}\left( \text{1 + }{{\text{r}}_{2}}*{{\text{t}}_{2}} \right)\text{ }....\text{(ii)} \\
\end{align}$

Dividing (i) by (ii) and putting the values of
$\begin{align}
  & {{\text{A}}_{1}}\text{ = 12122, }{{\text{r}}_{1}}\text{ = 0}\text{.08, }{{\text{t}}_{1}}\text{ = 2, }{{\text{r}}_{2}}\text{ = 0}\text{.09 and }{{\text{t}}_{2}}\text{ = }\dfrac{8}{3},\text{ we get,} \\
 & \dfrac{12122}{{{\text{A}}_{2}}}\text{ = }\dfrac{\left( 1\text{ + 0}\text{.08*2} \right)}{\left( 1\text{ + 0}\text{.09*}\dfrac{8}{3} \right)} \\
 & \Rightarrow \text{ }{{\text{A}}_{2}}\text{ = }\dfrac{12122\text{ x 1}\text{.24}}{1.16} \\
 & \text{ = 12958} \\
\end{align}$
Thus, we get the same answer for the final amount received, without finding the value of principal balance.