Question 1137628: You are working for a finance firm and a client comes to you and wants to know how much money they should put in an annuity (which earns 2.58% interest compounded quarterly) at the end of each three months for the next 49 years. Their goal is that when they retire at the end of 49 years, they would like the quarterly withdrawals from the annuity to total $60,000 per year and that the annuity is to last for the 20 years from when they retire. You are to determine the amount which your client needs to deposit into the annuity at the end of each three months for the next 49 years so that they can meet their retirement goal.
a.) show all work and label important steps and values.
b.) find the total amount of interest client will earn (from the time they start contributing to the account to when they make the last withdrawal).
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! this is what i get.
when they retire, it is assumed they will be withdrawing 15,000 at the beginning ofeach uarter for the next 20 years.
i used the following online calculator.
https://arachnoid.com/finance/
inputs to the calculator were:
present value = 0
future value = 0
number of time periods = 20 years * 4 quarters per year = 80 quarters
payment amount = 15,000 each quarter.
interest rate = 2.58% per year / 4 = .645% per quarter.
payment is made at the beginning of each quarter.
i click on pv and the calculator tells me that i need 941,163.53 to be in the account at the beginning of the investment period.
here's what the results look like.
i then took that amount and made the following inputs into the calculator.
present value = 0
future value = 941,163.53
number of time periods = 49 years * 4 quarters per year = 196 quarters
payment amount = 0
interest rate = 2.58% per year / 4 = .645% per quarter.
payment is made at the end of each quarter.
i click on pmt and the calculator tells me that the quarterly payments need to be 2,403.29.
here's what what the results look like.
when using the calculator, .....
if you input payments as positive, the present value or the future value will show up as negative.
if you input the payments as negative, the present value or the future value will show up as positive.
likewise, if you input the present value or the future value as positive, the payments will show up as negative, and vice versa.
negative values means money going out from you.
positive values means money coming in to you.
in the first calculation, the 15,000 payment was shown as positive because it was money coming in to you.
in the second calculation, the payment was shown as negative because it was money going out from you.
the assumption was that you started your retirement immediately after the last payment was made into the retirement fund and immediately received the first payment
of 15,000 from the retirement fund.
a different assumption might change the numbers a litle, but not very much.
for example, if i assumed end of quarter payments of 15,000, then the present value would be 935,131.93 rather than 941,163.53.
that, in turn would affect the payments required to get that future value.
it would require end of quarter payments of of 2387.89 rather than 2403.29.
the difference is the interest rate per quarter in both the present value calculations and the payment calculations.
2403.29 / 1.00645 = 2387.89.
2387.89 * 1.0645 = 2409.29.
941163.53 / 1.00645 = 935131.93.
935131.93 * 1.00645 = 941163.53.
based on the assumptions that i had, which were 15000 taken at the beginning of each quarter for 80 quarters, and 2403.29 given at the end of each quarter for 196 quarters, the answers i had were:
941,163.53 was required at the start of the end of the investment period which was the same as the start of the retirement period.
2403.29 was required to be paid at the end of each quarter during the investment period.
15000 was received at the beginning of each quarter during the retirement period.
as for the interest earned, .....
during the investment period, a total of 196 * 2403.29 was paid for a total payments value of payment of 471,044.84.
the value at the end of the investment period was 941,163.53.
the interest earned was therefore 941,163.53 minus 471,044.84 = 470,118.75 during the investment period.
the value at the beginning of the retirement period was 941,163.53.
1,200,000 was withdrawn during the retirement period (80 * 15000 = 1,200,000).
the difference was interest earned during the retirement period.
that was equal to 1,200,000 - 941,163.53 = 258,836.47.
total interest earned was 470,118.75 during the investment period plus 258,836.47 earned during the retirement period = 728,955.22.
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