Question

Simple interest on a sum of money is ₹ x after one year. The compound interest (compounded annually) at the same rate after one year is ₹ y. Which of the following is correct?

• A. x = y
• B. x - y = 0
• C. x + y = 1000
• D. None of these

Answer 1

Answer: (A), (B)

The correct options are
A

x = y

B

x - y = 0

The simple interest and compound interest (compounded annually) after one year on a certain sum will be the same.

We can verify it as well.
We know, for a principal P, rate of interest r and time t,
simple interest = $\frac{P\times r\times t}{100}$

Simple interest after one year, x
= $P\left[\frac{r}{100}\right]$

Similarly, compound interest
= $P{[1+\frac{r}{100}]}^n-P$

Compound interest after one year, y
= $P{[1+\frac{r}{100}]}^1-P$

$\Rightarrow$ y = $P+P\left(\frac{r}{100}\right)-P$

$\Rightarrow$ y = $P\left(\frac{r}{100}\right)$

$\Rightarrow$ x = y

$\Rightarrow$ x - y = 0