On January 1, 1980, your favorite uncle John turned 43 and started saving for his retirement. He invested $18,894.75 each year on January 1 until he turned 62 on 1/1/1999 (20 total deposits). Over the 20 years, he managed to earn an effective annual rate of return of 9.50%, and he assumed he could continue to earn that rate of return until he turned 90. Looking at his account balance, he calculated that he could immediately withdraw $74,050.56 to cover living expenses for 1999. And, going forward, he could withdraw that same amount on January 1 of each year, but adjusted for a 3% inflation. That is, in 2000, he could withdraw $74,050.56 x 1.03 $76,272.08; in 2001, $74,050.56 x 1.032 $78,560.24; etc. He planned on a Cotal of 28 withdrawals, with the last one of $164.487.70 on 1/1/2026 when he turned 89. At that point, the account balance would be zero. 501
On January 1, 1980, your favorite uncle John turned 43 and started saving for his retirement. He invested $18,894.75 each year on January 1 until he turned 62 on 1/1/1999 (20 total deposits). Over the 20 years, he managed to earn an effective annual rate of return of 9.50%, and he assumed he could continue to earn that rate of return until he turned 90. Looking at his account balance, he calculated that he could immediately withdraw $74,050.56 to cover living expenses for 1999. And, going forward, he could withdraw that same amount on January 1 of each year, but adjusted for a 3% inflation. That is, in 2000, he could withdraw $74,050.56 x 1.03 $76,272.08; in 2001, $74,050.56 x 1.032 $78,560.24; etc. He planned on a Cotal of 28 withdrawals, with the last one of $164.487.70 on 1/1/2026 when he turned 89. At that point, the account balance would be zero. 501
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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Transcribed Image Text:On January 1, 1980, your favorite uncle John turned 43 and started saving for his retirement. He
invested $18,894.75 each year on January 1 until he turned 62 on 1/1/1999 (20 total deposits).
Over the 20 years, he managed to earn an effective annual rate of return of 9.50%, and he assumed
he could continue to earn that rate of return until he turned 90.
Looking at his account balance, he calculated that he could immediately withdraw $74,050.56 to
cover living expenses for 1999. And, going forward, he could withdraw that same amount on
January 1 of each year, but adjusted for a 3% inflation. That is, in 2000, he could withdraw
$74,050.56 x 1.03 $76,272.08; in 2001, $74,050.56 x 1.032 $78,560.24; etc. He planned on a
total of 28 withdrawals, with the last one of $164.487.70 on 1/1/2026 when he turned 89. At that
point, the account balance would be zero.
501
On 1/1/2023, right after making his withdrawal for 2023, your uncle decided to become a Tibetan
monk. He left you the balance of his investment account. How much was in the account? Assume
he earned the 9.50% each year.
Enter your answer in dollars, truncated to the nearest dollar, with no punctuation. For example, if
your answer is $255,895.76, enter "255895". Note that Canvas may include commas.
Expert Solution
Step 1
The future value of an investment:
The value of a current investment at some finite, specified point of time in the future is known as its future value.
If the investments/withdrawals are made in fixed amounts at fixed intervals over a finite time periods the investments/withdrawals are known as annuities.
If the investments are made at the end of a period is known as an annuity.
If the investments are made at the beginnning at of a period, it is known as an annuity due.
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