Compound interest with a set amount withdrawn yearly....

[Burgerbasher]

OK so the problem I am working on is the following:

Deposit a set amount into an account (Dep). Receive yearly compounded interest (Int), following the interest being added withdraw a set figure as salary (Sal). What I am trying to figure out is how much will my account be worth after 30 years...

Some figures to play with

Dep (D) = 50,000,000
Int (I) =1.5%
Sal (S) =300,000

I can get so far with a formula but the grows ridiculously large:

D(1+I/100)-S after 1 year
D((1+I/100)-S)(1+I/100)-S after 2 years
D(((1+I/100)-S)(1+I/100)-S)(1+I/100)-S after 3 years etc...after 30 years it would be ridiculous

I have tried unsuccessfully to combine common factors

Any help would be greatly appreciated

 

[stapel]

What formula(s) did they give you for working with annuities?

Thank you!

 

[Ishuda]

OK so the problem I am working on is the following:

Deposit a set amount into an account (Dep). Receive yearly compounded interest (Int), following the interest being added withdraw a set figure as salary (Sal). What I am trying to figure out is how much will my account be worth after 30 years...

Some figures to play with

Dep (D) = 50,000,000
Int (I) =1.5%
Sal (S) =300,000

I can get so far with a formula but the grows ridiculously large:

D(1+I/100)-S after 1 year
D((1+I/100)-S)-S)(1+I/100 after 2 years
D(((1+I/100)-S)(1+I/100)-S)(1+I/100)-S after 3 years etc...after 30 years it would be ridiculous

I have tried unsuccessfully to combine common factors

Any help would be greatly appreciated

You are just deriving the regular annuity equation. Letting R(n) be the remainder after n years and x = 1+I/100 for easier 'writing',
R(1) = D x¹ - S (1)
R(2) = D x² - S (1 + x)
R(3) = D x³ - S (1+x+x²)
...
R(n) = D xⁿ - S (1+x+x²+...+x^n-1) after n years.

The sum is the sum of a geometric series which has a closed form solution