Financial Algebra Help!
Alistar has an annual income of $25,000. He decides to take classes on line and at night so that he can continue to work. After 3 years he gets his degree and immediately starts earning $32,000 per year. If it takes Alistar 6 years to recover his investment for his education, how much did it cost him?

Question

Financial Algebra Help!
Alistar has an annual income of $25,000. He decides to take classes on line and at night so that he can continue to work. After 3 years he gets his degree and immediately starts earning $32,000 per year. If it takes Alistar 6 years to recover his investment for his education, how much did it cost him?

lastdaywork · Answer

I would say 3*25K + 3*32K

mathmale · Answer

I think we have to state assumptions first, and one of them could be that interest is compounded annually.  We are told the jump in salary resulting from earning that degree is the difference between $32,000 and $25,000, or $7000.

Now I need (at least for myself) to make another assumption:  that we want to know how much our friend paid for his education, knowing that this amount, with interest paid over 6 years, increases to that $7000.

Let C be the cost of his education.  Then A=(7000)=C(1+r)^6, where r is the rate of return.  Unfortunately, this leaves us with only ONE equation in TWO unknowns, which is insufficient info with which to solve the problem as stated.

If, on the other hand, we arbitrarily chose the interest rate (rate of return) to be 0.05, it'd be relatively easy to calculate C:  7000=C(1+0.05)^6, or

$$C=\frac{ 7000 }{ 1.05^{6} }$$=$5,223.51.

Anyone able to question my assumptions and/or provide a different problem-solving perspectives?   If so, welcome aboard; please proceed.

mathmale · Answer

Ooops.  I overlooked that extra bit of data:  3 years is the time it took for our friend to earn his degree.

anonymous · Answer

ok thank you