Question

Mahesh borrowed rs 16000 at 7 1/2 % p,a simple interest. On the same day, he lent it to gagan at the same rate but compounded annually. What does he gain at the end of 2 years?

Answer 1

Answer :

$\begin{lgathered}\bold{Given} \begin{cases}\sf{Principal=Rs. 16000} \\ \sf{Rate=7 \dfrac{1}{2} \%= \dfrac{15}{2} \: p.a.}\\ \sf{Time=2\: Yr. }\end{cases}\end{lgathered}$

• According to the Question Now :

$\implies\tt{Gain = Compound \: Interest - Simple \:Interest}$

$\implies\tt{Gain = \bigg[P \bigg(1 + \dfrac{r}{100} \bigg)^{t} - 1 \bigg]- \bigg[\dfrac{PRT}{100}}\bigg]$

$\implies\tt{Gain = \bigg[16000 \bigg(1 + \cancel\dfrac{15}{200}\bigg)^{2} - 1 \bigg]- \bigg[\dfrac{\cancel{16000} \times 15 \times 2}{ \cancel{200}} }\bigg]$

$\implies\tt{Gain = \bigg[16000 \bigg(1 +\dfrac{3}{40}\bigg)^{2} - 1 \bigg]- \bigg[80 \times 15 \times 2}\bigg]$

$\implies\tt{Gain = \bigg[16000 \bigg(\dfrac{43}{40}\bigg)^{2} - 1 \bigg]- \bigg[80\times 30}\bigg]$

$\implies\tt{Gain= \bigg[16000 \bigg(\dfrac{1849}{1600} -1 \bigg) \bigg]- \bigg[2400}\bigg]$

$\implies\tt{Gain= \bigg[\cancel{16000} \times \dfrac{1849 -1600}{ \cancel{1600}}\bigg]- \bigg[2400}\bigg]$

$\implies\tt{Gain = \bigg[10 \times 249\bigg]-\bigg[2400}\bigg]$

$\implies\tt{Gain=Rs.(2490 - 2400)}$

$\implies\large\boxed{ \tt Gain =Rs. 90}$

∴ Mahesh will Gain Rs. 90 after 2 Years.