Question

Naresh puts 10,000 at interest compounded annually for 2 years. Had he invested it at 1% more rate of interest compounded annually, he would have earned 209 more. What is the interest rate? (1) 7% (2) 6% (3) 5% (4) 4%

Answer 1

Given:

• Naresh puts 10,000 at interest compounded annually for 2 years.
• Had he invested it at 1% more rate of interest compounded annually, he would have earned 209 more.

To find: the rate of interest

Solution:

• Let the rate of interest be x% per annum

• For the sum of Rs. 10000 compounded annually for 2 years, his income will be
• = Rs. $10000 \times (1 + \frac{x}{100})^{2} - 10000$

• When the rate of interest is 1% more i.e. (x + 1)%, his income will be
• = Rs. $10000\times (1+\frac{x+1}{100})^{2}-10000$

By the given condition,

$\quad 10000\times (1+\frac{x+1}{100})^{2}-10000=10000\times (1+\frac{x}{100})^{2}-10000+209$

$\Rightarrow 10000[(1+\frac{x+1}{100})^{2}-(1+\frac{x}{100})^{2}]=209$

$\Rightarrow 10000(1+\frac{x+1}{100}+1+\frac{x}{100})(1+\frac{x+1}{100}-1-\frac{x}{100})=209$

$\Rightarrow 10000(2+\frac{x+1}{100}+\frac{x}{100})(\frac{x+1}{100}-\frac{x}{100})=209$

$\Rightarrow 10000\times \frac{200+x+1+x}{100}\times \frac{x+1-x}{100}=209$

$\Rightarrow 2x+201=209$

$\Rightarrow 2x=8$

$\Rightarrow x=4$

Answer: Option (4) 4% is correct.