Question
In: Finance
A corporate treasurer wishes to accumulate a total of $50,000,000 forty years from today.
A corporate treasurer wishes to accumulate a total of $50,000,000 forty years from today. He plans to make equal semiannual deposits into an account earning 12 percent compounded quarterly. What must be the amount of these deposits, if the first deposit will be made exactly three from today (at the end of year 3) and the last deposit will be made six months before the $50,000,000 is needed?
Solutions
Expert Solution
Formula: The Future Value of an ordinary annuity (FV)
FV= C× {[(1+r)^n]-1}/r
FV = Future value (The cumulative amount available in Future) 50,000,000
C= Periodic cash outflow.
r =effective interest rate for the period. ((1+(0.12/4))^2)-1= 6.09%
n = number of periods. 40*2- 2.5*2 = 75
50,000,000= C× {[(1+0.0609)^75]-1}/0.0609
C = $36,575.40 (Answer).
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