Question

I borrowed ₹ $12,000$ from Jamshed at $6\% $per annum simple interest for $2$years. Had I borrowed this sum at $6\% $ per annum compound interest, what extra amount would I have to pay?

Answer 1

Hint: We will calculate simple interest for principal ₹ $12,000$ $r = 6\% $ and T$ = 2$years. Further, we will complete the amount. Thereafter, we will calculate the amount for the compound interest formula.
By using simple interest (SI) $ = \dfrac{{P \times R \times T}}{{100}}$
And amount $ = SI + P$
Amount $ = P{\left( {1 + \dfrac{R}{{100}}} \right)^T}$
Here, P $ = $Principal sum
R$ = $ Rate of interest
T$ = $Time


Complete step by step solution:
Here P$ = $ ₹ $12,000$
 R$ = 6\% $
T$ = 2$years
We will calculate SI by using the formula:
 (SI) $ = \dfrac{{P \times R \times T}}{{100}}.........\left( i \right)$
We will substitute the value of P, R and T in the equation (i), we have
SI $ = \dfrac{{12000 \times 6 \times 2}}{{100}}$
SI $ = 120 \times 6 \times 2$
SI $ = 12 \times 120$
SI $ = 1440$
Now, Amount $ = SI + P$
Amount $ = $ ₹ $1440 + 12,000$
Amount $ = $ ₹ $13440.00$
Now, we will calculate amount for the formula of compound interest, we have
Amount $ = P{\left( {1 + \dfrac{R}{{100}}} \right)^T}$
We will put the value of P, R and T in above formula, we have
Amount \[ = 12000{\left( {1 + \dfrac{6}{{100}}} \right)^2}\]
Amount \[ = 12000{\left( {1 + \dfrac{3}{{50}}} \right)^2}\]
Amount \[ = 12000{\left( {\dfrac{{50 + 3}}{{50}}} \right)^2}\]
Amount $ = 12000 \times {\left( {\dfrac{{53}}{{50}}} \right)^2}$
Amount $ = 12000 \times \dfrac{{53}}{{50}} \times \dfrac{{53}}{{50}}$
Amount $ = 120 \times \dfrac{{53}}{5} \times \dfrac{{53}}{5}$
Amount $ = \dfrac{{24 \times 53 \times 53}}{5}$
Amount $ = \dfrac{{24 \times 2809}}{5}$
Amount $ = \dfrac{{67416}}{5}$
Amount $ = 13,483.20$
$\therefore $By using simple interest amount $ = $₹ $13440.00$
And by using compound interest amount $ = $₹ $13483.20$
Extra amount $ = $compound interest amount $ - $simple interest amount
Extra amount $ = $₹ $13483.20 - 13440.00$
Extra amount $ = $₹ $43.20$


Note: In these types of questions, one should carefully solve the amount while calculating the amount, the formula of amount has different simple interest and compound interest.