Question

Find the principal that yields a simple interest of rs 40 or compound interest of rs  41 at the same rate of interest per annum in 2 years.

Answer 1

Answer: RS. 400

Step-by-step explanation:

SI for 2 years =Rs. 40

CI for 2 years = Rs.41

$SI =\dfrac{P\times R\times T}{100} \\\\\Rightarrow 40 = \dfrac{P\times R \times 2}{100} \\\\\Rightarrow 2000= P\times R$

Now

$CI = A- P \\\\A= CI+P \\\\\Rightarrow CI+P = P(1+\dfrac{R}{100} )^2\\\\\Rightarrow 41+P= P(1+\dfrac{2000}{P\times 100 } )^2\\\\\Rightarrow 41+P= P(1+\dfrac{20}{P} )^2\\\\\Rightarrow 41+P = P(\dfrac{(P+20)^2}{P^2} )\\\\\Rightarrow 41P+P^2=P^2+40P+400\\\\\Rightarrow P = 400$

Hence, the Principe is Rs. 400

Answer 2

The principal is Rs.400

Step-by-step explanation:

Let the principal be x and rate of interest be r

Simple interest = Rs.40

$SI = \frac{P \times T \times R}{100}\\40=\frac{x \times 2 \times r}{100}\\\frac{40 \times 100}{2x}=r ---- 1$

Compound interest = 41

Amount = Compound interest + Principal = 41+x

$Amount = P(1+\frac{r}{100})^t \\41+x= x(1+\frac{r}{100})^2 \\100(\sqrt{\frac{41+x}{x}}-1)=r ---2$

Equate 1 and 2

$\frac{40 \times 100}{2x}=100(\sqrt{\frac{41+x}{x}}-1)\\x=400$

Hence The principal is Rs.400

#Learn more:

Find the compound interest at the rate 10% per annum for 2 years on the principal which in 2 year at the rate 10% per annum yields rs 200 as simple interest

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