Answer:
15 years
Explanation:
Future value of Lumpsum = PV (1 + i)^n
PV = Present value = $4,500
i = interest rate = 8.5%
n = no. of compounding period = 15 years
So, FV = 4,500 * (1 + .085)^15
= 4,500 * 3.3997428788
= $15,298.84
When Eleanor choose to pay $500 for annual membership fee:
Future Value of annuity due = (1 + r) * P[((1 + r)n - 1) / r]
where P = Periodic payment = $500
i = interest rate = 8.5%
n = no. of compuding period = 15 years
So, FV of annuity due = (1 + .085) * 500[((1 + .085)^15 - 1) / .085]
= (1.085) * 500[(3.3997428788 - 1) / .085]
= (1.085) * 500 * 28.2322691624
= $15,316.01
So, within 15 years lifetime membership is cheaper than annual membership.
