Question

suppose you are the financial manager of the International Emirates University IEU. And you are requested at the end of the year 2020 to pay 30,000 as the building rent for the coming two years. Furthermore at the end of the year 2022 you are requested to renew the university working licenses with total amount of $ 50,000 for the coming two years. Also, at the end of the year 2023 you have to face withdraw of $80,000 to pay well-known fees to the head of university in Dubai. If you can earn 8% in your fund how much you should deposit by today to reach your goals, and to leave your balance zero after the last withdrawal?

Answer 1

So what this is is
many words

assuming year 0 is 2017

so compound first thing till 2020, take out 30000
the remaining is copmpounded til 2022, take out 50000
remaining is compounded for 1 more year and that is equal to 80000

so from 2017 to 2020, that is 5 years
from 2020 to 2022 is 2 years
from 2022 to 2023 is 1 year


work backwards

A=P(r+1)^t
last one
A=80000
P=?
r=0.08
t=1 year

80000=P(1.08)^1
divide both sides by 1.08
I would leave in fraction
20000000/27=P

now that is the remaining after paying 50000, after 2 years of compounding

so
50000+(2000000/27)=P(1.08)^2
solve using math
about
106374=P

now reverse back

5 years
paid 30000

30000+106374=P(1.08)^5
solve using math
92813.526=P
round
$92813.53




put $92813.53 in the fund