Question 1190445: A. For all parts of this problem, money is invested in a retirement account with an APR of 8.04%. (This is close to the average annual return rate for a traditional individual retirement account over the last decade.) You want to be able to withdraw $24,000 per year for 20 years after retirement. Round up to the cent for each answer.
3. How much must you have in the account to start with if compounding and withdrawals are both quarterly?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! for the yearly withdrawals:
annual payment = 24000 at the beginning of each year, or at the end of each year.
interest rate = 8.04% per year.
number of years = 20.
if the withdrawals are at the beginning of each year, the present value will be equal to 253,824.62.
if the withdrawals are at the end of each year, the present value will be equal to 234,935.78.
for the quarterly withdrawals:
quarterly payment = 24000 / 4 = 6000 at the beginning of each quarter, or at the end of each quarter.
interest rate = 8.04% each year / 4 = 2.01% per quarter.
if the withdrawals are at the beginning of each quarter, the present value will be equal to 242,537.94.
if the withdrawals are at the end of each quarter, the present value will be equal to 237,758.99.
all input and outputs were rounded to the nearest penny, as instructed.
it was not given that the withdrawals would be at the end of each time period or at the beginning of each time period, so i gave you both.
with quarterly compounding, the interest rate per year is divided by 4 and the number of time periods is multiplied by 4.
let me know if you have any questions.
theo
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