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Question 1151782: Ishan and Hazel plan to retire at age 60 with a retirement income of $48,000 a year from their savings. Rather than pay themselves the whole amount at the beginning of each year, they have decided that payment at the beginning of each quarter of $12,000 gives them the right balance of flexibility and maximized interest earnings. They feel they can safely earn an interest rate of 8%, compounded quarterly, on their money and they are budgeting based on the prediction that they will live until they are 90 years old.
How much money will they have to have saved by the time they are 60 in order to reach their retirement goal? [1]
If the same total calculated above was to be saved, but no interest earned whatsoever, how much would be available to live on each quarter? [2]
If the full 30 years are lived and quarterly budget spent, how much money in total will have been utilized in retirement? [3]
How much will have been earned in interest? [4]
Now that Ishan and Hazel have their saving goal calculated they want to start budgeting to reach that goal. They are 40 years old, so they have just 20 years to save up the total they calculated they would require so that they can still reach their goal of retirement by age 60.
If they assume the same interest rate, and make deposits into their savings at the beginning of every month, how much would their deposit have to be each month?[1]
How much interest will be earned? [2]
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! ishan and hazel will retire at 60 and expect to live to 90.
that would be 30 years.
8% per year compounded quarterly = 8% / 4 = 2% per quarter.
30 years * 4 = 120 quarters.
they expect to receive 12,000 at the beginning of each quarter (48,000 per year divided by 4 = 12,000 per quarter).
the money that they need to invest at the beginning of their retirement period would be $555,249.96.
i used the following online calculator to provide the answer.
https://arachnoid.com/finance/index.html
my inputs were:
present value = 0
future value = 0
number of periods = 30 years * 4 quarters per year = 120 quarters.
payment amount = 12,000
interest rate per period, % = 8% per year / 4 = 2% per quarter.
payments are to be made at the beginning of each quarter.
i then click on PV and the calculator tells me that the amount of money required at the beginning of the investment period is equal to $555,149.96.
the total money that ishan and hazel will receive during their retirement period is $12,000 per quarter * 120 quarters = $1,440,000.
the interest that they earned during their retirement period is equal to $1,440,000 minus $555,149.96 = $884,850.04.
if $555,149.96 was saved, but no interest was able to be earned on it, then the amount of money available at the beginning of each quarter of their retirement period would be equal to $555,149.96 / 120 = $4626.25.
since they are now 40, then they have 20 years in which to have $555,149.96 available at the beginning of their retirement period.
the same interest rate per year is used, but the payment are being made at the beginning of each month, therefore the interest rate is compounded monthly rather than quarterly.
i make the following inputs into the financial calculator.
present value = 0
future value = $555,149.96
number of periods = 20 years * 12 months per year = 240 months.
interest rate per period, % = 8% / 12 = .666666667% per month.
payments are made at the beginning of each monthly period.
i then click on payment amount and the calculator tells me that the amount of money that needs to be invested at the beginning of each month is equal to $936.26
240 * $936.26 = total payments of $224,702.4
the interest earned is therefore $555,149.96 minus $224,702.4 = $69,552.44.
the following picture shows the inputs and output for the calculation of the money required to be available at the beginning of the retirement period.
the following picture shows the inputs and outputs for the calculation of the amount of money that needs to be invested at the beginning of each month in order to have the amount of money needed at the beginning of the retirement period.
the following two pictures show the beginning and ending quarterly withdrawals during the retirement period.
this was done in excel.
the following two pictures show the beginning and ending monthly deposits prior to the retirement period.
this was also done in excel.
eoq = end of quarter.
rembal = remaining balance
pmt = payment
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