if $ 85 is put in account that gets 8.5% and I add $15 at the end of each year how much will I have at the end of 8 years

Thanks Tetration your way will work well.

Here is another way :)

 

if $ 85 is put in account that gets 8.5%pa and I add $15 at the end of each year how much will I have at the end of 8 years

 

the 85$ will grow to  85*(1.085)^8

The first 15 will grow to 15(1.085)^7

The second 15 will grow to 15(1.085)^6

........

The last 15 only just goes in the bank so it will be 15

 

$$\\15+15(1.085)+15(1.085)^2 .........15(1.085)^7$$

This is a GP  a=15 r=1.085 n=8

 

$$\\S_n=\frac{a(r^n-1)}{r-1}\\\\
S_8=\frac{15(1.085^8-1)}{1.085-1}\\\\
S_8=\frac{15(1.085^8-1)}{0.085}\\\\$$

 

so total =  $$85(1.085)^8+\frac{15(1.085^8-1)}{0.085}\\\\$$

 

$${\mathtt{85}}{\mathtt{\,\times\,}}{\left({\mathtt{1.085}}\right)}^{{\mathtt{8}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{15}}{\mathtt{\,\times\,}}\left({{\mathtt{1.085}}}^{{\mathtt{8}}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}{{\mathtt{0.085}}}} = {\mathtt{325.710\: \!957\: \!814\: \!451\: \!144\: \!3}}$$

 

After 8 years it will be    $325.00

After zero years (at the beginning) you have $85:

 

a(0) = 85 

 

For each year that passes, the amount of money is multiplied by 1.085, and then $15 is added. 

 

a(n) = 1.085 * a(n - 1) + 15

 

 

 

We get:

 

a(1) = 1.085 * a(0) +15 = 1.085 * 85 +15 = 107.225 ≈ 107.26

a(2) = 1.085 * 107.26 + 15 ≈  131.34

 

And so forth until a(8) = ...