Question

$\huge\red{QUESTION:}$
If the difference of the CI and the SI on a sum of money for 2 years is 1% of the sum of money then find the annual rate of interest.​
$\huge\green{Thank \: you!! }$​

Answer 1

Step-by-step explanation:

The other answer given is correct but I will formulate it differently in case that helps some readers

Firstly CI is compound interest

SI is simple interest

We are asked to solve for the rate r which in two years has a future value (1 + r )^2 and has we calculated the future value using Simple interest method it be 1% less

Therefore CI - SI = 0.01

So,

(1+r)^2 - (1 + 2 r ) = 0.01

Expand to

1+ 2r + r^2 -1 -2r = 0.01

r^2 = 0.01

therefore r = 0.01)^1/2

r = 0.10. Or 10%

$\huge\pink{Thank \: you}$

Answer 2

$\huge\mathfrak{\underline{\underline{Answer:-}}}$

The other answer given is correct but I will formulate it differently in case that helps some readers

Firstly CI is compound interest

$\mathrm\orange{SI\: is\: simple\: interest\:}$

We are asked to solve for the rate r which in two years has a future value (1 + r )^2 and has we calculated the future value using Simple interest method it be 1% less

$\mathrm\purple{Therefore \:CI - SI \:= 0.01\:}$

$\mathrm\orange{So\: you\: can\: solve\: (1+r)^2\: - (1 + 2 r ) \:= 0.01}$

$\mathrm\purple{Expand\: to\: 1+ 2r + r^2 -1 -2r = 0.01\:}$

$\mathrm\orange{r^2 = 0.01\: therefore\: r = 0.01\:)^1/2\:}$

${\huge{\boxed{\overline{\mid{\purple{10\:percent\:}}}}}}$