I want to calculate how much as a percentage of my current income I must save/invest in order to have a pot of money, the interest on which will provide me in real dollars 80% or even n% of my current income.
Here is what I have so far, but the right side of the equation is really just the 80% - the pot of money part is missing. Also, I guess solving quadratic equations is not like riding a bicycle, and I can’t remember how to simplify these.
( x * salary ) ( 1 + i ) ( 1 + r – i ) ^ n = (.8 * salary ) ( 1 + i ) ^ n
where
x= the percentage of your current year salary one must save/invest in order to have an annual income of 80% of one’s salary
I’m not so sure about your equation. I plugged some numbers in and got some odd results. So I started from scratch. If you just want the simplified equation, I can’t help you. If you want to check out some numbers, read on.
t = length of retirement
n = number of withdrawals per year
P = annual retirement income
r = APR the leftover money will be getting
I gave a half-hearted attempt at simplifiying it and then simply put it into Excel.
Then I used another equation to determine how much I would have to put away each paycheck to save that amount:
B = P[(1 + r/n)^nt - 1]/[(1 + r/n) - 1]
t = years until retirement
n = number of paychecks per year
P = amount saved each paycheck
r = APR earned
You could set A = B and then solve for whatever you want, but remember that the variables have different meanings in each equation.
I created a nice Excel spreadsheet to plug numbers in and see the results. If you want me to send it to you, I will.
What I am trying to do is understand through an equation the relationship betweent the amount one must save as a percentage of income. Its interesting how savings rates vary dramatically from country to country - about 40% in Singapore and less than 4% in the U.S.