Question

John borrowed Rs.1,00,000 at 10 percent per annum simple interest. He immediately lent the whole sum at 10 percent per annum compound interest. At the end of 2 years, he would gain -

• A. Rs.1,000
• B. Rs.1,800
• C. Rs.2,000
• D. Rs.100.

Answer 1

The correct option is A Rs.1,000

Principal Amount borrowed $=Rs$ $1,00,000$.

Money is borrowed at S.I.

$T=2$ years

$R=10\%$

In simple interest, we know that the amount $\left(A\right)=P(1+\frac{R\times T}{100})$

$\therefore$ Amount after two years $=1,00,000(1+\frac{2\times 10}{100})$

$=1,00,000\times \frac{6}{5}$

$=1,20,000$

The borrowed money is lent by John on C.I. at same rate for same time.

In CI, we know that the amount $\left(A\right)=P{(1+\frac{R}{100})}^T$

$\therefore$ Amount that John will receive $=1,00,000{(1+\frac{10}{100})}^2$

$=1,00,000{\left(\frac{11}{10}\right)}^2$

$=1,21,000$

$\therefore$ John will get $1,21,000$ while be will have to pay $1,20,000$

$\therefore$ Gain $=Rs$ $(1,21,000-1,20,000)$

$=Rs$ $1,000$

Hence, John will gain $Rs.1000$.