# Differential equations interest probelm

1. Nov 26, 2012

### atrus_ovis

1. The problem statement, all variables and given/known data
Two same aged people P1,P2 create bank accounts at ages 25,35 respectively, and add 2000 euros annualy , for 10,30 years respectively. No initial capital in the accounts.

1.For interest 8% , what's the balance of each acount at age of 65 of P1,P2?
2.What should be the interest for the above balances to be equal

3. The attempt at a solution
I guess continuous interest is assumed.

The problem here is the constant 2000/year.
The interest r affects the balance in the form of
$$S_r(t) = S_0e^{rt}$$ , while the constant deposits $$S_{c0}(t) = S_{c0} + 2000t$$

edit : To the result of the bank's interest over a year, 2000 is added and the total is considered the balance for the application of interest at the next year.
Does it hold to say:
$$\frac{dS}{dt} = (2000+S)r \iff S(t) = S_0 e^{rt} + 2000rt$$ ?

Do i have to combine them somehow / write the relation as a DE and find the solution?
hints?

Last edited: Nov 26, 2012
2. Nov 26, 2012

### atrus_ovis

I think i got it:
$$S(t) = e^{rt}+2000rt+2000t$$

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