Question

Giving 20 points out for this question!

Answer 1

Answer: £20 doubling at the end of each year for 5 years

From the question, Stephen would want to select one option which gives the highest amount of profit. I mean, even if you were to select one, you would obviously try calculating all the 4 choices to see which one makes you earn the most money. Now let's conduct the workout and see which one will earn us the most £ in 5 years:

Option 1:

`(500*(5)/(100) ) + 500 ---- > 1yr\\= 25 + 500 \\ = 525\\\\(525*(5)/(100) ) + 525 ----- > 2yrs\\= 26.25 + 525\\= 551.25\\\\(551.25 * (5)/(100)) + 551.25 - - - > 3yrs\\ = 27.563 + 551.25\\= 578.813\\\\(578.813 * (5)/(100)) + 578.813 - - > 4 yrs\\ = 28.941 + 578.813\\ = 607.754 \\\\(607.754 * (5)/(100)) + 607.754 - - > 5 yrs\\ = 30.388 + 607.754\\ = 638.142 \\`

ans: £ 638.142

Option 2:

`1 year = 12 months\\5 years : 5*12 = 60 months\\\\10*60 = 600`

ans: £ 600

Option 3:

`(550*(3)/(100)) + 550 - - - - > 1yr\\= 16.5 + 550\\= 566.5 \\\\(566.5 * (3)/(100)) + 566.5 - - - > 2 yrs\\ = 16.995 + 566.5\\= 583.495\\\\(583.495 * (3)/(100)) + 583.495 - - > 3 yrs\\ =17.505 + 583.495\\= 601\\\\(601 * (3)/(100)) + 601 - - - - - - > 4 yrs\\= 18.03 + 601\\= 619.03\\\\( 619.03* (3)/(100)) + 619.03 - - - - > 5 yrs\\= 18.571 + 619.03\\= 637.601`

ans: £ 637.601

Option 4:

`20*2= 40 - - - - > 1yr\\40 * 2= 80 - - -- > 2 yrs\\80*2 = 160 - - - > 3 yrs\\160*2 = 320 - - - > 4 yrs\\320*2= 640 - - - > 5yrs`

ans: £ 640

Out of all the calculated answers, you can see that option 4 has the highest amount. So that's it. By the way, I might do some incorrections in some calculations because I am not good at long maths, but yes i hope I did it all right!

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hope it helped
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