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 A - $3,552.72

Step-by-step explanation:

Given :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%

To find : which account will yield the largest future value for Ethan, and how much greater that value will be than that of the other account.

Solution :

We find the future value of both.

Formula of annuity,

1) The first is an IRA where monthly payments are made, in the amount of $416.66, for 30 years and compound interest rate is 2.5%.

Monthly payment are made.

So, P=$416.66

Rate r=

Time t= 30 years

Substitute the value in the formula,

Future value of first is $223066.24

2) The second is a Roth IRA where annual payments are made, in the amount of $5000, for 30 years.compound interest rate is 2.5%.

Annual payment are made.

So, P=$5000

Rate r=

Time n= 30 years    

Substitute the value in the formula,

Future value of second is $219513.515

The largest future value is in the first IRA i.e, $223066.240

And how much the greater value is

IRA by 223066.240-219513.515=3552.72

IRA by $3552.72

Therefore, Option A is correct.

answer: the four apples you took away.

step-by-step explanation:

explanation:

step-by-step explanation: