Compound Interest Question. Max is planning to take three years off work to travel the world. He plans to start this holiday in 5 years time and is...

Let Max invest P.

Then P in
5years with compound interest becomes = (1.083^5)P .

After
that he should recieve $ 35000 for the first year of his travel. Then the balance = $
{(1.085^5)P -35000}.

For the next year the above balance,
(1.083^5)P - 35000 becomes with interest = [(1.083^5P- 35000]1.083 and Max Recieves
$35000  for the 2nd year of the travel.

Now  the balance is
$ [(1.083)^5*P -35000](1.083)-35000. And this balance earns interest and along with
interest it  becomes {[(1.083^5 P - 3500)1.083 -35000] 1.83 }  and he recieves another
$35000 and at this point his balance should be zero
.

Therefore 1.083^7*P - 350001.083^2-35000*1.083 -35000 =
0.

Or  P = 35000 (1.083^2+1.083+1) =
35000*3.255889

Therefore P = 3500*3.255889/(1.083^7) =
65214 dollars.

Therefore he should invest 
$65214 sothat recieves $35000 each of the 3 years and at the end the balance is
zero.

Tally : $ 65214 becomes with 8.3%
compound interest in 5 years = 65214*1.083^5 =
$97159.

After recieving $35000, the balance is
$(97159-35000) = $62159.

$(62159) becomes with 8.3%
compound interest for 1 year = $62159*1.083 = $67
318.

After recieving $35000 , the balance to earn interest
in 2nd year is  $(67318 -35000) = $32318.

$ 32318 should
becomes along with interest at the end of the 2nd year $(3218)*(1.083) =
$35000.

So Max takes $35000 for the 3rd year travel and now
the balnce is zero.