Question

The difference between simple interest and compound interest compounded annually on a certain sum is Rs.448 for 2 years at 8 percent per annum. Find the sum.

Answer 1

Since, C.I.
= A - P

C.I. = ${\displaystyle {(1+\frac{8}{100})}^2-\text{P}}$

= ${\displaystyle \text{P}{\left(\frac{108}{100}\right)}^2-\text{P}}$

= ${\displaystyle \frac{11664\text{P}}{10000}-\text{P}}$

= ${\displaystyle \frac{11664\text{P}-10000\text{P}}{10000}}$

= ${\displaystyle \frac{1664\text{P}}{10000}}$

S.I. = ${\displaystyle \frac{\text{P}\times 8\times 2}{100}}$

= ${\displaystyle \frac{16\text{P}}{100}}$

Now, C.I. - S.I = Rs.448

⇒ ${\displaystyle \frac{1664\text{P}}{10000}-\frac{16\text{P}}{100}}$ = Rs.448

⇒ ${\displaystyle \frac{1664\text{P}-1600\text{P}}{10000}}$ = Rs.448

⇒ 64P = Rs.4480000
⇒ P = Rs.70000
Hence, the sum is Rs.70000.