Question

a money lender lent out rs 10000 for 2 years at 16% per annum the interest rate being compounded annually. how much more he could earn if the interest be compounded half yearly​

Answer 1

Answer:

use the formula.

A=p{1+R/100}to the power of n

Answer 2

AnswEr :

• Principal = Rs.10000
• Rate = 16% p.a.
• Time = 2 Years

$\mathsf{CI = P \bigg(1 + \dfrac{r}{100} \bigg) ^{t} - 1}$

$\mathsf{CI = 10000 \times \bigg(1 + \dfrac{16}{100} \bigg) ^{2} - 1}$

$\mathsf{CI = 10000 \times \bigg(1 + \dfrac{4}{25} \bigg) ^{2} - 1}$

$\mathsf{CI = 10000 \times \bigg( \dfrac{29}{25} \bigg) ^{2} - 1}$

$\mathsf{CI = 10000 \times \bigg( \dfrac{841}{625} - 1 \bigg)}$

$\mathsf{CI = 10000 \times \dfrac{216}{625}}$

$\mathsf{CI = 16 \times 216}$

$\mathsf{CI = Rs. \: 3456}$

• If it will be Compounded Half Yearly then we have to decrease rate by half and increase time by twice :

• Principal = Rs. 10000
• Rate = 8% p.a.
• Time = 4 Years

$\mathsf{CI = P \bigg(1 + \dfrac{r}{100} \bigg) ^{t} - 1} \:$

$\mathsf{CI = 10000 \times \bigg(1 + \dfrac{8}{100} \bigg) ^{4} - 1}$

$\mathsf{CI = 10000 \times \bigg(1 + \dfrac{2}{25} \bigg) ^{4} - 1}$

$\mathsf{CI = 10000 \times \bigg( \dfrac{27}{25} \bigg) ^{4} - 1}$

$\mathsf{CI = 10000 \times \bigg( \dfrac{531,441}{390,625} - 1 \bigg)}$

$\mathsf{CI = 10000 \times \dfrac{140816}{390625}}$

$\mathsf{CI = Rs. \: 3605}$

• He will Earn Much More is :

⇒ CI₁ – CI₂

⇒ Rs. 3605 – Rs. 3456

⇒ Rs. 149

⠀

$\therefore$ If he gave money at half yearly then he earns Rs. 149 more.