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A cash flow at time zero (now) of $14,551 is equivalent to another cash flow that is an EOY annuity of $2,700 over seven years (starting at year 1). Each of these two cash-flow series is equlvaient to a third serie which is a unitom gadent series what is the value ofGfor this third series over the same seven-year trmo rterval? Assume that the ash flow the end of year one is zero. Choose the comect answer below O A. $089 O B. $77 O c. $295 O D. $1,450 E. Not enough informaton given
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Answer #1

Answer:

Let r be the interest rate

n=7 years

PV of annuity =2700*(1-(1+r)^-7)/r

Given PV of annuity=$14,551

2700*(1-(1+r)^-7)/r=14551

r=7%

So FV of $14551 =$23,366

Since FV of Gradient =G*[{(1+r)^n-1}/r^2 - n/r]=G*[{1+7%)^7-1}/7%^2-7/7%]=23.63G

Given FV of Gradient=FV of $14551

23.63G=23366

G=$988.83

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