You have 4 different investment options

4% interest
7% compound continuously
19% annually
5% every month

You have 1000 dollars

how long does it take for the value to double in each other investment options?

How long does it take until 1000 becomes 1800?

What does the 1000 dollars become after 10 years with each investment plan?

1 answer

The amount you start with does not matter, as long as it doubles
e.g. 10000 ---> 2000
1 ----> 2

I will do the 19% case, you do the others

1(1.19)^t = 2
1.19^t = 2
take log of both sides and use log rules
t log 1.19 = log 2
t = log2/log1.19 = appr 3.985 years

7% compound continuously ----- takes special care
1e^(.07t) = 2
now take ln of both sides, remember lne = 1
.07t lne = ln2
.07t = ln2
t = ln2/.07 = appr 9.9

let me know what you get for the others.