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

Option (1) is correct.

Account with  investment (1) of monthly payments amount of $416.66, for 30 years at a rate of 2.5% will yield the largest future value for Ethan.

Investment (1) will give $3,552.72 greater value than that of the other account.

Step-by-step explanation:

Given : Ethan is planning for his retirement. He has narrowed it down to two investment options.

We have to find  account that will yield the largest future value for Ethan, and  how much greater that value will be than that of the other account.

We know future value will be

Where FV is future value,

P is monthly payment

r is rate of interest

n is time period

For investment (1)

monthly payments amount of $416.66, for 30 years at a rate of 2.5%

Here, monthly payment = $416.66

Time = 30 × 12 = 360 months

rate = 2.5% =

Substitute, we get,

For  investment  (2)

annual payments of amount of $5000, for 30 years interest at a rate of 2.5%.

thus, annual payment = $5000

Time = 30 years

rate = 2.5% =

Thus,  account with  investment (1) of monthly payments amount of $416.66, for 30 years at a rate of 2.5% will yield the largest future value for Ethan.

Difference = 223066.24047-219513.5158 = 3552.72467

Thus, Investment (1) will give $3,552.72 greater value than that of the other account.

Option (1) is correct.

ok then what happened.