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Joe wants to start an SEP-IRA that will have $460,000 in it when he retires in 15 years. How much should he invest semiannually in his IRA to do this if the interest is 15% compounded semiannually?

Answer :

jepessoa

Answer:

$4,448.77

Explanation:

time until retirement = 15 years x 2 semiannual contributions = 30 payments

interest rate =15% / 2 = 7.5%

future value = $460,000

we can use the future value of an annuity formula:

future value = payment x annuity factor

FV annuity factor 7.5%, 30 periods = 103.3994

payment = future value / annuity factor

payment = $460,000 / 103.3994 = $4,448.77

The amount that should be invested is $4,448.77.

Calculation of the amount:

Since

time until retirement = 15 years x 2

= 30 payments

And,

interest rate =15% / 2 = 7.5%

Also,

future value = $460,000

Now we can use the future value of an annuity formula:

Here,

future value = payment x annuity factor

where,

FV annuity factor 7.5%, 30 periods = 103.3994

So,

payment = future value / annuity factor

= $460,000 / 103.3994

= $4,448.77

hence, The amount that should be invested is $4,448.77.

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