Question

Sudhir lent ₹25000 at a compound interest at 10% payable yearly , which lent ₹ 25000 at compound interest at 10% payable half yearly .Find the difference in the interest received by Sudhir and prashant at the end of the one year.​

Answer 1

Answer: 5

Step-by-step explanation:

Given:

(i) Sudhir lent 2000 Rupees at compound interest at 10% payable yearly.

(ii) Prashant lent 2000 Rupees at compound interest at 10 percent payable half yearly.

To find:

(i) The difference in the interest received by Sudhir and Prashant at the end of one year.

Solution:

Amount (A) in CI is given as:

A = P(1 + r/n)^(nt)

P is the Principal money

R is the rate percentage

t is time period

n is number of times interest is compounded per unit t

For Sudhir,

A = 2000(1 + 0.10)^1

= 2000(1.1)

= Rs 2200

CI = A-P

= Rs (2200-2000)

= Rs 200

For Prashant,

A = 2000(1 + 0.10/2)^(1*2)

= 2000(1.05)^2

= Rs 2205

CI = A-P

= Rs (2205-2000)

= Rs 205

Difference in interests = Rs 205- Rs 200

= Rs 5

I think this is right...

Answer 2

Solution :

$\underline{\bf{Given\::}}}}$

Sudhir lent Rs.25000 at a compound Interest at 10%  payable yearly, which Prashant lent Rs.25000 at compound interest at 10% payable half - yearly;

$\underline{\bf{Explanation\::}}}}$

$\underbrace{\bf{In\:Sudhir\:Case\::}}}$

Using formula of the compounded annually;

$\boxed{\bf{Amount=Principal\bigg(1+\frac{R}{100} \bigg)^{n} }}}}$

A/q

$\longrightarrow\sf{A=25000\bigg(1+\cancel{\dfrac{10}{100}} \bigg)^{1}}\\\\\\\longrightarrow\sf{A=25000\bigg(1+\dfrac{1}{10} \bigg)^{1}}\\\\\\\longrightarrow\sf{A=25000\bigg(\dfrac{10 + 1}{10} \bigg)^{1} }\\\\\\\longrightarrow\sf{A=2500\cancel{0} \times \dfrac{11}{\cancel{10}} }\\\\\\\longrightarrow\sf{A=Rs.(2500\times 11)}\\\\\longrightarrow\bf{A=Rs.27500}$

Now;

$\longrightarrow\sf{C.I. = Amount - Principal}\\\\\longrightarrow\sf{C.I. = Rs.27500 - Rs.25000}\\\\\longrightarrow\bf{C.I. = Rs.2500}$

$\underbrace{\bf{In\:Prashant\:Case\::}}}$

Using formula of the compounded half - yearly;

$\boxed{\bf{Amount=Principal\bigg(1+\frac{R}{2*100} \bigg)^{2n} }}}}$

A/q

$\longrightarrow\sf{A=25000\bigg(1+\dfrac{\cancel{10}}{2\times 10\cancel{0}} \bigg)^{(2 \times 1)}}\\\\\\\longrightarrow\sf{A=25000\bigg(1+\dfrac{1}{20} \bigg)^{2}}\\\\\\\longrightarrow\sf{A = 25000 \bigg(\dfrac{20 + 1}{20} \bigg)^{2} }\\\\\\\longrightarrow\sf{A= 25000 \bigg(\dfrac{21}{20} \bigg)^{2} }\\\\\\\longrightarrow\sf{A= 25000\times \dfrac{21}{20} \times \dfrac{21}{20} }\\\\\\\longrightarrow\sf{A = \dfrac{\cancel{25000}\times 21 \times 21}{\cancel{400} }}$

$\longrightarrow\sf{A= Rs.(62.5 \times 21\times 21)}\\\\\longrightarrow\bf{A= Rs.27562.5}$

Now;

$\longrightarrow\sf{C.I. = Amount - Principal}\\\\\longrightarrow\sf{C.I. = Rs.27562.5 - Rs.25000}\\\\\longrightarrow\bf{C.I. = Rs.2562.5}$

Thus;

$\mapsto\sf{Difference = Prashant\:_{(Interest)} - Sudhir\:_{(Interest)}}\\\\\mapsto\sf{Difference = Rs.2562.5 - Rs.2500}\\\\\mapsto\bf{Difference = Rs.62.5}$

∴ The difference in the Interest received by Sudhir & Prashant will Rs.62.5 at the end of one year .