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atrus_ovis
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Homework Statement
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
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
[tex]S_r(t) = S_0e^{rt}[/tex] , while the constant deposits [tex] S_{c0}(t) = S_{c0} + 2000t [/tex]
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:
[tex] \frac{dS}{dt} = (2000+S)r \iff S(t) = S_0 e^{rt} + 2000rt[/tex] ?
Do i have to combine them somehow / write the relation as a DE and find the solution?
hints?
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