SOLUTION: You think you need $1.5 million and your retirement advisor thinks you will average 6% a year on your account. How much will you need to contribute a year to your account if you ha

Question 1123824: You think you need $1.5 million and your retirement advisor thinks you will average 6% a year on your account. How much will you need to contribute a year to your account if you have 40 years to your retirement?

Found 3 solutions by Theo, ikleyn, MathTherapy:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
number of time periods = 40 years * 12 months per year = 480 months.

interest rate per time period = 6% / 12 = .5% per month.

you have nothing to start with.

you want to have 1.5 million dollars in the account at the end of the 40 year period.

using a financial calculator, you would make the following inputs.

present value = 0
future value = 1,500,000 (entered without the commas)
number of time periods = 480
percent interest per time period = .5
payments are made at the end of each time period.

you would then have the calculator compute the payment.

using the online financial calculator at https://arachnoid.com/finance/, the calculator will tell you that the monthly payment will be $753.20 at the end of each month.

the future value is shown as positive because it's money you will receive.
the payment are shown as negative because it's money you will pay out at the end of each month.

disregard the negative sign.
the payment is $753.20 at the end of each month for the next 40 years.

here are what the inputs and outputs from the use of the online calculator look like.

when you make your inputs, you don't enter the commas.
the calculator puts them in there when it provide the display after you tell it to calculate for you.

Answer by ikleyn(52790)   (Show Source): You can put this solution on YOUR website!
.

        The problem asks about annual payments, assuming that the account is compounded annually.

        The tutor @Theo gave a solution for monthly payments, assuming that the account is compounded monthly.

        Obviously, it is the solution to the different problem.

        So, I came to solve the problem and to answer the question as it was posed in the post.

It is a classic Ordinary Annuity saving plan. The general formula is FV = , where FV is the future value of the account; P is annual payment (deposit); r is the annual percentage yield presented as a decimal; n is the number of deposits (= the number of years, in this case). From this formula, you get for for the annual payment P = . (1) Under the given conditions, FV = $1,500,,000; r = 0.06; n = 40. So, according to the formula (1), you get for the annual payment P = = $9692.30. Answer. The necessary annual deposit value is $9692.30.

---------

On Ordinary Annuity saving plans, see the lessons
    - Ordinary Annuity saving plans and geometric progressions
    - Solved problems on Ordinary Annuity saving plans
in this site.

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

You think you need $1.5 million and your retirement advisor thinks you will average 6% a year on your account. How much will you need to contribute a year to your account if you have 40 years to your retirement?

Annual payments for the next 40 years:
RELATED QUESTIONS
You think you need 1.5 million and your retirement advisor thinks you will average 8% a... (answered by Aldorozos,MathTherapy)
If you have $500,000 in your retirement account and you are currently making 5% interest... (answered by ewatrrr)
You want to be able to withdraw $40,000 from your account each year for 25 years after... (answered by greenestamps)
You are currently making $70,000 a year after taxes and are interested in maintaining... (answered by Aldorozos)
You are currently making $80,000 a year after taxes and are interested in maintaining... (answered by jorel555)
If you have $40,000 in your retirement account,and you are currently making 8% interest... (answered by Aldorozos)
If you have $400,000 in your retirement account, and you are currently making 8% interest (answered by Theo)
If you have $400,000 in your retirement account, and you are currently making 8%... (answered by Theo)
You want to be able to withdraw $40,000 from your account each year for 30 years after... (answered by Theo)