Don won the “Cash for Life” lottery and will receive a $1000 per week for the next 25 years. How much must the lottery corporation invest today into an account that pays 4% compounded weekly to provide Don with the prize?
+171 tricky line
google says there are approx 52 weeks in a year; knowing that we can find how much they are paying in a year:
$1000 \times 52 = 52000$$
we can also approx find how much they are going to pay for 25 years:
$ 52000\times 25= 1300000 $$
we know that the compounded interest formula is $ A=P\left(1+\frac{r}{n}\right)^{n t} $ where $P$ is the ammount that is getting invested, which means we have to solve for it:
$ A=P\left(1+\frac{r}{n}\right)^{n t} \ \ \Rightarrow \ \ \ \ \ P= \frac{A}{\left(1+\frac{r}{n}\right)^{nt}} $
we have $A=1300000$$ ; $ n=52 $ ; $ t=25 $ ;
$r=4\% \ \ \Rightarrow \ \ \ r=0.o4$
just plug and chug at this point:
$P=\frac{1300000}{\left(1+\frac{0.4}{52}\right)^{52\times 25}}$
$ P=\frac{1300000}{(1.0076923)^1300} $
$ P=\frac{1300000}{21199} $
$ P=61\frac{6861}{21199} $ or $ P=61.6861 $
