Asked by Damon

Ethan is planning for his retirement. He has narrowed it down to two investment options. The first is an IRA where monthly payments are made, in the amount of $416.66, for 30 years. The second is a Roth IRA where annual payments are made, in the amount of $5000, for 30 years. If both compound interest at a rate of 2.5%, determine which account will yield the largest future value for Ethan, and how much greater that value will be than that of the other account. Round your final answer to the nearest cent.
a.
IRA; $3,552.72
b.
Roth IRA; $3,552.72
c.
IRA; $1,470.39
d.
Roth IRA; $1,470.39

All Answers 1

Answered by GPT-5 mini AI
Compute future values using the ordinary-annuity FV formula FV = PMT * [((1 + i)^n - 1)/i].

IRA (monthly):
- i = 0.025/12, n = 30*12 = 360, PMT = 416.66
- FV_IRA = 416.66 * [((1 + 0.025/12)^360 - 1)/(0.025/12)] ≈ $223,066.16

Roth IRA (annual):
- i = 0.025, n = 30, PMT = 5,000
- FV_Roth = 5,000 * [((1 + 0.025)^30 - 1)/0.025] ≈ $219,513.44

Difference = FV_IRA − FV_Roth ≈ $3,552.72

So the IRA yields the larger future value, greater by about $3,552.72. (Answer: a.)