Question

hari purchased relief bonds for rs. 1000, a sum which will fetch him rs.2000 after 5 years. find the rate of interest if the interest is compounded half yearly​

Answer 1

Answer:

14.34%

Step-by-step explanation:

Given:

The sum of money = Rs. 1000

Amount fetched after 5 years = Rs. 2000

To find:

The rate of interest if the interest is compounded half-yearly

Solution:

We know that the formula to calculate the amount if the interest is compounded half-yearly is as follows:

=>{A = P [1+ \frac{\frac{R}{2} }{100} ]^2^n}}

Now, by substituting the given values in the formula, we get

2000 = 1000 [1+ \frac{\frac{R}{2} }{100} ]^2^\times^5}}

=> 2 = [1+ \frac{\frac{R}{2} }{100} ]^2^\times^5}}

=> 2 = [1+ \frac{R }{200} ]^1^0}}

taking root of 10 on both sides

=>sqrt[10]{2} = 1 + \frac{R}{200}⟹ 102

=1+ 200R

using calculator→ \sqrt[10]{2}

10

2

= 2^\frac{1}{10}2

101= 1.0717

=> 1.0717 = 1+\frac{R}{200}⟹1.0717=1+ 200R

=> 1.0717 -1 = \frac{R}{200}⟹1.0717−1= 200R

=> R = 0.0717 \times 200⟹R=0.0717×200

=>{R = 14.34\%}⟹R=14.34%

Thus, the rate of interest if the interest is compounded half-yearly is 14.34%.