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Henry wants to save a fixed amount each month for 12 years and then withdraw $950 each month for the next 2 years to fund his round the world trip. How much does he need to save for himself each month if he can earn 11% compounded monthly?
can you please explain how do you do this?

2006-12-03 09:23:35 · 2 answers · asked by huseyinarslan 1 in Science & Mathematics Mathematics

2 answers

This is a somewhat complicated question.

There is a formula called the "annuity formula". I found a derivation for it at http://mathforum.org/library/drmath/view/54617.html, if you want to try to follow it.

It is:

S = P[(1+i)^n - 1]/i

where:
P is the monthly payment
i is the MONTHLY interest rate, and
n is the number of months

You need to use the formula twice, first to figure out how much money needs to be in the account when he starts withdrawing, and then how much he needs to contribute to get to that point.

So, if he's withdrawing $950 per month for 24 months, P = -950, n = 24, i = .11.

S = -$950[(1.11)^24 -1]/.11 = -$97,065.44

So at the point he starts withdrawing, he'll need $97,065.44.

To get that amount, solve again, this time for P, with n = 5x12 = 60.

$97,065.44 = P[(1.11)^60 - 1]/.11 = 2758.924P
P = $35.18 per month

That's not a lot of money to earn almost $100k...but then again, you'll never find a bank account that will give you 11% interest per month either.

2006-12-03 09:48:45 · answer #1 · answered by Jim Burnell 6 · 0 0

does henry's money continue to compound after he's withdrawn some?

2006-12-03 17:38:24 · answer #2 · answered by grigri9 2 · 0 0

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