A new car is selling for $5000$ down and $5000$/year (at the end of) each of the next $5$ years. If interest rates are $5$% compounded semi-annually, what is the fair price of the car in cash?
What I did was make a formula for the Future Value:
$$A(t) = 5000 + 5000 \, \left(1 + \frac{0.05}{2}\right)^{2t}.$$
I plugged in $t = 5$ into the equation and got
$$A(5) = 11400.42.$$
Is this right?
$i^{(2)}=5\%$ so the effective annual interest is $i=(1+5\%/2)^2-1\approx 5,06\%$. The present value is $$ A(0)=5000+5000v+\cdots+5000v^5=5000\;\ddot a_{\overline{6}|i}=18,258.93 $$ where $v=\frac{1}{1+i}\approx 0.952$.