Juan has an annuity that pays him $9400 at the beginning of each year. Assume the economy will grow at a rate of 3.4% annually. What is the value of the annuity if he received it now instead of over a period of 10 years?

Answer 1

Method1
Since the basic formulas for annuity assume payments at the end of a period, a slight adjustment is needed.
PV = 9400 +9400(1 - 1.034^-9)/.034
= 81243.05

method 2.
look at the geometric series
9400 + 9400(1.034^-1) + 9400(1.034^-2) + ... + 9400(1.034^-9)
here a = 9400, r = 1.034^-1
sum = a(1 - r^10)/(1-r)
= 9400(1 - 1/1.034)^10/(1-1/1.034)
= 9400(.28419519)/.032882011)
= 81243.05, same as before

Answer 2

Thank you very much