Question

Given that the interest is only earned on principal, if an investment of Rs. $1000.00$amount to Rs. $1440.00$in two years, then what is the rate of interest earned?

Answer 1

Hint: Interest can be defined as the amount of money paid for using someone else’s money. Also, the amount received is the sum of the investment and the interest received. Here, we will use the formula for simple interest.

Complete step-by-step solution:
Investment, $I = 1000{\text{ Rs}}{\text{.}}$
Amount, $A = 1440{\text{ Rs}}{\text{.}}$
Term, $T = 2$years
Amount, $A = I + SI$
Place the values in the above expression –
$1440 = 1000 + SI$
Make the required term the subject –
 $\Rightarrow 1440 - 1000 = SI$
Simplify the above expression –
$\Rightarrow SI = 440$Rs. ….. (A)
Simple interest can be calculated by using the formula –
$\Rightarrow SI = \dfrac{{PRT}}{{100}}$
Where, I is the Simple Interest, P is the Principal, R is the rate of the interest and T is the term period.
$\Rightarrow 440 = \dfrac{{1000R(2)}}{{100}}$
Common factors from the numerator and the denominator cancels each other.
$\Rightarrow 440 = 20R$
Term multiplicative on one side if moved to the opposite side, then it goes to the denominator.
$\Rightarrow R = \dfrac{{440}}{{20}}$
Simplifying the above expression finding the division of the terms-
$\Rightarrow R = 22\% $

Hence, rate of interest earned is $22\% $

Note: Always convert the percentage rate of interest in the form of fraction or the decimals and then substitute further for the required solutions. Remember the difference between simple interest and compound interest and apply its concept wisely. Compound interest can be defined as the interest paid for the interest earned in the previous year. Be good in multiples and do simplification carefully. Always remember that the percentage is expressed as the fraction to the hundredth.