I need help understanding the solution given for this problem. Some alternate ways to do the problem would be helpful as well. I need to find the growth rate of a growing annuity.
Problem: Assume that you will be saving each year for 3 years, starting next year. If your first year savings is $2,500, at what constant rate must your savings grow each year to hit your target of $12,000 at the end of four years if your savings earn 5% per annum?
Solution given to me: 2,500(1+.05)^3 + 2,500(1+g)(1+.05)^2*(1+.05)^1 = 12,000
(1+g)^2 + 1.05(1+g)-3.46989 = 0
g = 41.01%
It's great that they gave me the solution yet I have no idea how they got it. I can't seem to solve that equation for g. If anyone could help, I'd greatly appreciate it.
Is there an easier way to do this? There has to be a way to calculate for g using a financial calculator. Thanks in advance!