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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?

 Jun 25, 2021
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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  $

 Jun 25, 2021

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