Payments of $1000 are deposited into a fund every six months and the account earns 10% interest, compounded semi-annually. How much is in the fund immediately after the 20th payment is made?
I'm aware on how to solve this, just really unsure of my common ratio that I computed, which is 2.1. Am I on the right track? Thank you!
Note that the $k$th payment is made after $(k-1)\cdot 6$ months with respect to the first payment. Hence the first deposit of $1000$ dollars at the $20$th payment is increased to $1000\cdot 1.1^{19}$. The second deposit of $1000$ dollars at the $20$th payment is increased to $1000\cdot 1.1^{18}$. Recall that if $r\not=1$ then $$r^0+r^1+r^2+\dots +r^{n-1}=\frac{r^n-1}{r-1}.$$ Can you take it from here?