How much would $100 invested at 6% interest compounded continuously be worth after 20years? round your answer to the nearrest cent

6% interest means 6% of the money in the account is added each year.

With an initial value of $100, that means $6 is added after 1 year.

It's easiest to just make an exponential function for this.

The format of this is f (x) = a (b) ^x

a is the y-intercept/starting value, which in this case is $100.

b is the rate of change, which is 6% in this case.

When something increases by a percent, you add 100% to that.

This means there is a rate of change of 106%, which translates to 1.06 in the function.

Plugging in the variables you get:

f (x) = 100 (1.06) ^x

x is time.

After 1 year, x=1.

After 2 years, x=2.

And so on and so forth.

To find the value of the account after 20 years, plug in 20 for x.

f (x) = 100 (1.06) ^20

First, you would solve 1.06^20, which equals about 3.20713547.

Then just multiply that by 100.

3.20713547 • 100 = 320.713547

Last, you just need to round to the nearest cent.

320.713547 - > 320.71

So the answer is that the account is worth $320.71 after 20 years with a 6% interest rate.