You are planning to make monthly deposits of $475 into a retirement account that pays 10 percent interest compounded monthly. If your first deposit will be made one month from now, how large will your retirement account be in 30 years

$1,073,731.76

Explanation:

This question refers to an annuity which is the payment of a series of cash.

It relates to the future value of an annuity because the question asks what the retirement income will be in 30 years.

The formula for the future value of an annuity is,

F = P * ([1 + r]^n - 1 )/r

Where,

P is the payment amount.

r is equal to the interest (discount) rate and

n is the number of periods.

As the details given to us are in a yearly format but the payments are monthly we would need to convert these details as well.

r = 0.10/12

= 0.10/12

It's best to leave it as a fraction

n = 30 * 12 months

= 360 months.

Now we plug them into the formula.

= 475 * ( (1+(0.1/12))^360 - 1)/(0.1/12)

= $1,073,731.76

This is the value in 30 years.

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