A major drug company anticipates that in future years it could be involved in li

Question

A major drug company anticipates that in future years it could be involved in litigation regarding perceived side effects of one of its antidepressant drugs. To prepare a war chest, the company wants to have money available 6 years from now that has a present worth today of $50 million. The company expects to set aside $6 million in the first year and uniformly increasing amounts in each of the next 5 years. If the company can earn 12% per year on the money it sets aside, by how much must it increase the amount set aside each year to achieve this goal?

Please show work.

Explanation / Answer

Suppose it incerases by g

so

50,000,000 = 6,000,000/1.12 + 6,000,000*(1+g)/1.12^2 + 6,000,000*(1+g)^2/1.12^3 + 6,000,000*(1+g)^3/1.12^4

+ 6,000,000*(1+g)^4/1.12^5 + 6,000,000*(1+g)^5/1.12^6

50/6 = 1/1.12 *[ 1+(1+g)/1.12 + (1+g)^2/1.12^2 +......(1+g)^5/1.12^5 ]

28/3 = [(1+g)^6/1.12^6 - 1]/((1+g)/1.12 - 1)

Put (1+g)/1.12 = t

so we have (t^6 -1)/(t-1) = 28/3

3*t^6 - 3 = 28*t -28

3*t^6- 28*t +25 =0

t = 1 or t= 1.1754

g = 0.12 = 12%

or g = (1.1754)*1.12 -1 = =0.31645 = 31.645 %

ans cannot be 12%

so ans is 31.645 % .....

g = 31.65 %........(ans)

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