Question

a ammount become twice in 5 years on compound interest. in how many times it will be 8 time if the rateof interest remains same?

Answer 1

let the principal be x. Rate = y%. As it becomes twice in 5 years on compound Interest, then we get =>
$2x = x{( 1 + y})^{5}$
=>
$2 = {( 1+ y)}^{5} ...(1)$
So the amount becomes 8x in a years .=>
$8x = x {( 1+ y)}^{a} = > 8 = {(1 + y)}^{a} ...(2)$
On cubing the equation on both sides, we get =>
${2}^{3} = ({(1 + y)}^{5})^{3} = > 8 = {(1 + y)}^{15}.$
So on comparing equation (2)with the above equation, we get a=15 years . So in 15 years on compound Interest , we get 8 times the amount we invested at first .Hope it helps you...Mark me as Brainliest.