To supplement your planned retirement in exactly 35 years, you estimate that you
ID: 2740223 • Letter: T
Question
To supplement your planned retirement in exactly 35 years, you estimate that you need to accumulate $250,000 by the end of 35 years from today. You plan to make equal, annual end-of-year deposits into an account paying 8% annual interest. How large must the annual deposits be to create the $250,000 fund by the end of 35 years? if you can afford to deposit only $750 per year into the account, how much will you have accumulated by the end of the 35th year? You just won a lottery that promises to pay $1,000,000 exactly 10 years from today. Because the $1,000,000 payment is guaranteed by the state you live in, opportunities exist to sell the claim today for an immediate single cash payment. What is the least you will sell your claim for if you can earn a 6% rate of return on similar risk investments during the 10-year period? What is the least you will sell your claim for if you can earn a 9% rate of return on similar risk investments during the 10-year period? What is the least you will sell your claim for if you can earn a 12% rate of return on similar risk investments during the 10-year period? You plan to retire (again) in exactly 20 years. Your goal is to create a fund that will allow you to receive $20,000 at the end of each year for the 30 years between retirement and death(a psychic told you would die exactly 30 years after you retire).you know that you will be able to earn 11% per year during the 30-year retirement period. How large a fund will you need when you retire in 20 years to provide the 30-year, $20,000 retirement annuity ? How much will you need today as a single amount to provide the fund calculated in part a if you earn only 9% per year during the 20 years preceding retirement?Explanation / Answer
8.
a.
Calculation of annual deposit:
b.
Calculation of FV after 35 years:
9.
a.
Least lump-sum amount to sell the claim of lottery with 6% interest:
b.
Least lump-sum amount to sell the claim of lottery with 9% interest:
c.
Least lump-sum amount to sell the claim of lottery with 12% interest:
10.
a.
For example, $20,000 need 21st year, with 11% interest, the PV is calculated as follows.
For 22nd to 50th year also you have to calculate like the above (for 22nd year where n=2, r=115).
For short cut method:
FV of annuity =
The amount must be in account at the end of 20 years from now to be able to earn $20,000 for year for next 30 years would be $173,876.
b.
PV needed to today with 9% interest is calculated as follows.
You must have $31,024.85 today invested to have $173,876 20 years from now.
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