There is a Future Value of Annuity function built into excel. You can set it up with the following example of 10% APY compounding daily, 5 days of compounding, and 1% of the $1000 added every single day
A1 = 0.1/365
A2 = 5
A3 = 1000 * 0.01
=FV(A1, A2, -A3)
This will give a final value of $50.03 in your account after 5 days which you can easily check ...
"suppose I had $1000 as an initial investment, by day two I would have $1010. That $10 would then be rolled into the 10% APY account. This cycle would repeat every day."
It sounds like you are effectively putting $10 into a 10% (let's say daily) account, every day.
a = 10
r = 0.1
Totalling up the balance x over days. (Assuming the $10 would be ...
Applying the standard loan equation derived here:
r = 13.5/100/4
s = 140000
n = 4*10
d = r (1 + 1/(-1 + (1 + r)^n)) s = 6429.28
r = periodic interest rate
s = principal
n = number of periods
d = periodic payment
You can rule out answer #1 immediately: there are 40 withdrawals, and 40 x 3500 is 140,000, the original deposit. This would be the answer if there was no interest, but there is interest, so this answer is wrong.
Now you can also rule out answer #2, because it is less than answer #1, and earning interest will enable Vanessa to withdraw more than not earning ...
You have the right idea. Euler's number e links all continuously compounded growth/decay functions in that it represents the amount by which and initial amount will grow (decay) if one continuously compounds (decays) 100% per unit period.
In the equation you give, you would want r to be the per unit interest rate (meaning monthly interest if that is what you ...
You can get an estimate of the real rate of return after taxes by using:
(13% - 5%) * (1-15%) = 8% * 85% = 6.8%
or just take out the intermediate parts that cancel out:
((((1+13%)^10-1)*85%+1)^(1/10)/(1+5%) -1 = 6.42%