QUESTION 9
Suppose you plan to retire at age 70, and you want to be able to
withdraw an amount of $83,000 per year on each birthday from age 70
to age 100 (a total of 31 withdrawals). If the account which
contains your savings earns 5.4% per year simple interest, how much
money needs to be in the account by the time you reach your 70th
birthday? (Answer to the nearest dollar.)
Hint: This can be solved as a 30-year ordinary annuity plus one
withdrawal at age 70, or as a 31-year annuity due.
5 points
QUESTION 10
Today is your 25th birthday, and you have calculated that you need to accumulate $1 Million by your 70th birthday in order to retire in a manner in which you are accustomed to living. If your retirement account earns 8% per year simple interest, how much must you deposit on each of your birthdays (from 26 to 70) in order to reach your target retirement savings on your 70th birthday? (Answer to the nearest dollar.)
5 points
QUESTION 11
Suppose you plan to retire at age 70, and you want to be able to withdraw an amount of $6,000 per month beginning with the first month after your 70th birthday until you reach your birthday at age 100. If the account which contains your savings earns 5% APR compounded monthly, how much money needs to be in the account by the time you reach your 70th birthday? (Answer to the nearest dollar.)
5 points
QUESTION 12
Today is your 25th birthday, and you want to save $2.4 Million by your birthday at age 70. If you expect to earn 7% APR compounded monthly in your retirement account, what constant payment at the end of each month must you deposit into the account through your 70th birthday in order to reach your retirement savings goal on your 70th birthday? (Answer to the nearest penny.)
5 points
QUESTION 13
A 8.7% coupon bearing bond pays interest semi-annually and has a maturity of 16 years. If the annual yield to maturity is 5.2%, what is the current price of this bond? (Answer to the nearest penny.)
Q9. Number of Periods = 31
Rate = 5.4%
Annuity due = 83,000
Value of fund at retirement = (1+r)*annuity*
(1-(1+r)^{-n})/r =
(1+5.4%)*83000*(1-(1+5.4%)^{-31})/5.4% = 1,302,740
Q10. Rate =8%
Number of periods = 35
FV of fund = 1,000,000
Amount of deposit = FV/((1+r)^{n}-1)/r =
1,000,000/((1+8%)^{35}-1)/8% = 5803
Q11. Rate per month = 5%/12
Number of Periods = 12*30 = 360
Annuity = 6000
PV of fund = Annuity*(1-(1+r)^{-n})/r =
6000*(1-(1+5%/12)^{-360})/(5%/12) = 1,117,689.70
Q12. Number of Periods = 35*12 = 420
Rate per month = 7%/12
FV = 2,400,000
PMT = FV/((1+r)^{n}-1)/r =
2,400,000/((1+7%/12)^{35}-1)/(7%/12) =1333
Max 4 subparts can be solved.
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