Financial matters and indices

[IB<3]

Hey, since my Norwegian math-language is horrible I'm posting this in English.

This is the question:

Giuseppe borrows 15000 euro to buy a car. The bank charges 5% interest compounded yearly. Giuseppe agrees to pay two-thirds of the amount owing at the end of each year. How much would Giuseppe have paid back at the end of 5 years?

This is how far I've gotten:

u[sub]1[/sub]=(2/3)(15000*1.05)
u[sub]2[/sub]=(2/3)(1/3)(15000*0.5)

r=1/3

But when I put it into the formula to find the sum of a geometric sequence, I GET THE WRONG ANSWER!

Please help!

[IB<3]

u2=(2/3)(1/3)(15000*1.05)

[Andreas345]

[tex]a_1=15000\cdot \frac{2}{3}\cdot 1.05[/tex]

[tex]a_2=\left (15000\cdot \frac{2}{3}\cdot 1.05 \right)\cdot \frac{2}{3}\cdot 1.05 \\ ...\\...[/tex]
[tex]a_n=15000\cdot 0.7^n[/tex]