Question

What sum of money will amount to $Rs.1234$ in $2$ years at $10\% $ per annum compound interest?

Answer 1

Hint: For the compound interest we first calculate the interest of the starting period and add it to the amount borrowed, and then we calculate the interest for the next period by a new amount. Hence using the compound interest formula, we are easily able to find the required answer.

Complete step by step solution:
The compound interest can be calculated using the formula, $A = P{(1 + \dfrac{r}{{100}})^n}$
Here P is the amount borrowed, n is the time period and A is the final amount in total.
Since the amount to be paid after $2$ years is $Rs.1234$ and thus $A = Rs.1234$ and the time is $n = 2$ years.
The compound interest per annum is given as $10\% $ thus $r = 10\% $
Thus, we need to find the required principal amount, but substituting all the known values into the given formula, thus we have $A = P{(1 + \dfrac{r}{{100}})^n} \Rightarrow 1234 = P{(1 + \dfrac{{10}}{{100}})^2}$
Further solving we get $1234 = P{(\dfrac{{110}}{{100}})^2} \Rightarrow 1234 = P{(\dfrac{{11}}{{10}})^2}$
Squaring the values, we have $1234 = P \times \dfrac{{121}}{{100}}$
Further simplifying by putting the value P is one side and all other terms in another side we get $1234 = P \times \dfrac{{121}}{{100}} \Rightarrow P = 1234 \times \dfrac{{100}}{{121}}$
Thus, we get $P = 1234 \times \dfrac{{100}}{{121}} \Rightarrow P = Rs.1019.83$
Therefore, the required principal amount is $Rs.1019.83$

Note: There are a total of two types of interest and they are called as simple interest and compound interest.
Interest is the amount that we paid after the regular interval of the given time that borrowed as the rent for the money lent.
$n$ is the number of times interested in the compound in years.
Moneylenders lend or the bank money to the people is needed to gain more money at the time of repayment because of the interest on the money lent.