Question

Suppose $500 is invested at 6% annual interest compounded continuously. When will the investment be worth $1000?

Answer 1

Number of years `=11.9`

Number of years = 11 years and 11 months

Explanation:

Given -

Present amount `=$500`
Future amount `=$1000`
Annual Interest `=6% 0r 0.06`

Formula to calculate Compound interest `A=P(1+r)^n`

Solve the equation for `n`
`P(1+r)^n=A`
`(1+r)^n=A/P`

`n log(1+r)=log(A/P)`

`n=(log(A/P))/(log(1+r))=(log(1000/500))/(log(1+0.6))=030103/0.025306=11.895`

Number of years `=11.9`

Number of years = 11 years and 11 months