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?

All i really have to know is how to figure out the monthly plan.

after m months, the monthly plan has a balance of

1000(1 + .05)^m
so, to make it to 1800, you have
1000(1.05)^m = 1800
1.05^m = 1.8
m log1.05 - log1.8
m = log1.8/log1.05 = 12.04
so, it will take about a year

To figure out how long it takes for the value to double in each investment option, you can use the compound interest formula:

A = P * (1 + r/n)^(n*t)

Where:
A = the final amount
P = the principal amount (initial investment)
r = the annual interest rate (in decimal form)
n = the number of times interest is compounded per year
t = the number of years

For each of the investment options:

1) 4% interest:
To double the value, we need to find when the amount becomes 2000 dollars. So, A = 2000 and P = 1000. Substituting these values into the formula, we get:
2000 = 1000 * (1 + 0.04)^t

To solve for t (the number of years), we can take the natural logarithm (ln) of both sides, and solve for t:
ln(2000/1000) = t * ln(1.04)
t = ln(2) / ln(1.04)

2) 7% compounded continuously:
The formula for continuous compound interest is A = P * e^(r*t), where e is the mathematical constant approximately equal to 2.71828. Using the same approach as above, we need to solve for t when A = 2000:
2000 = 1000 * e^(0.07*t)

To solve for t, divide both sides by 1000 and take the natural logarithm of both sides:
ln(2) = 0.07*t
t = ln(2) / 0.07

3) 19% annually:
Again, we need to solve for t when A = 2000, using the same formula as above:
2000 = 1000 * (1 + 0.19)^t

Taking the natural logarithm of both sides gives:
ln(2) = t * ln(1.19)
t = ln(2) / ln(1.19)

4) 5% every month:
Since interest is compounded monthly, n = 12 (12 months in a year). We need to solve for t when A = 2000:
2000 = 1000 * (1 + 0.05/12)^(12*t)

Taking the natural logarithm of both sides gives:
ln(2) = t * ln(1 + 0.05/12)
t = ln(2) / (12 * ln(1 + 0.05/12))

To find out how long it takes until 1000 becomes 1800, you can substitute A = 1800 in the formulas above and solve for t for each investment option.

To find out what the 1000 dollars become after 10 years with each investment plan, you can substitute t = 10 in the formulas above and solve for A for each investment option.

I hope this explanation helps you understand how to calculate the monthly investment plan.