SOLUTION: Amy contributed $1011.00 at the end of every six months for 21.5 years into an RRSP earning interest at 6.65% compounded semi-annually. Seven years after the last contribution, Amy
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-> SOLUTION: Amy contributed $1011.00 at the end of every six months for 21.5 years into an RRSP earning interest at 6.65% compounded semi-annually. Seven years after the last contribution, Amy
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Question 1207546: Amy contributed $1011.00 at the end of every six months for 21.5 years into an RRSP earning interest at 6.65% compounded semi-annually. Seven years after the last contribution, Amy converted the RRSP into an RRIF that is to pay her equal quarterly amounts for 17.25 years. If the first payment is due three months after the conversion into the RRIF and interest on the RRIF is 7.66% compounded quarterly, how much will Amy receive every three months? Answer by Theo(13342) (Show Source):
present value = 0
future value = 0
number of semi-annual time periods = 21.5 * 2 = 43
interest rate per semi-semi-annual time period = 6.65% / 2 = 3.325%.
payment at the end of each semi-annual time period = -1011
this is negative because it's what you invest.
calculator says future value = 93699.84998.
this amount is then invested for an additional 7 years.
input to the calculator for the second part.
present value = -93699.84998.
this is negative because it's what you invest.
number of semi-annual time periods = 7 years * 2 = 14
interest rate per semi-annual time period is the same at 3.325%
payment at the end of each semi-annual time period = 0.
calulator says that the future value at the end of the investment period = 148120.3368.
input to the calculator for third part:
present value = -148120.3368
future value = 0
number of semi-annual time periods = 17.25 years * 4 = 69
interest rate per quarterly time period = 7.66 = 4 = 1.915%
payment is made at the end of each quarterly time period.
calculator says that the payment at the end of each quarterly time period = 3886.306912.
i used excel to confirm the results are accurate as i understood the problem.
here are the results.
the results confirm the calculator results are correct.
the amount in the account at the end of the first investment period = 93669.84998.
that was at the end of time period 43 in excel.
the amount in the account at the end of the second investment period = 148120.3368.
that was at the end of time period 14 that came after time period 43.
i started the time period counting over after each investment period to keep them separate from the investment period that came before.
the first investment time periods and the second investment time periods were both semi-annual with the same semi-annual interest rate of 3.325%.
the remaining balance in the account at the end of the second investment period was used to calculate the amount to be withdrawn at the end of each quarter in the third investment period.
the amount to be withdrawn was calculated to be equal to 3886.306912.
the start of the withdrawal period was at the end of time period 14 which came after time period 43.
3886.306912 was withdrawn at the end of each quarterly time period for 69 time periods.
the remaining balance in the account at the end of the 69 quarterly periods was equal to 0, meaning that the account was fully withdrawn.
the answer to your problem is that amy will withdraw 3886.31 when rounded to the nearest penny.
i'll be available to answer any questions you might have.
