BEGIN MODE
N
10
I
8%
PMT
-$100
FV
$0
PV
$724.69
Assume that you are offered an annuity that pays $100 at the end of each year for 10 years.
You could earn
8% on your money in other equally risky investments.
What is the most you should pay for the annuity?

SECTION 4-11
SOLUTIONS TO SELF-TEST
N
10
I
7%
PV
$100,000
FV
$0
PMT
-$14,237.75
How would your answer change if you made withdrawals at the beginning of each year?
BEGIN MODE
N
10
I
7%
PV
$100,000
FV
$0
PMT
-$13,306.31
I
7.0%
PV
$100,000
PMT
-$10,000
FV
$0
N
17.8
How long would they last if you earned 0%?
I
0.0%
PV
$100,000
PMT
-$10,000
FV
$0
N
10.0
How long would they last if you earned the 7% but limited your withdrawals to $7,000 per year?
I
7.0%
PV
$100,000
PMT
-$7,000
FV
$0
N
#VALUE!
N
12
PMT
-$12,000
PV
$100,000
FV
$0
I
6.11%
BEGIN MODE
N
10
PMT
-$10,000
PV
$60,000
FV
$0
I
13.70%
If you think a “fair” rate of return would be 6%, how much should you ask for the annuity?
BEGIN MODE
N
10
I
6%
PMT
-$10,000
FV
$0
PV
$78,016.92
Suppose you inherited $100,000 and invested it at 7% per year.
How large of a withdrawal could you
make at the end of each of the next 10 years and end up with zero?
If you had $100,000 that was invested at 7% and you wanted to withdraw $10,000 at the end of each
year, how long would your funds last?
* This result means that with $7,000
withdrawals, you would never exhaust the
funds.
Your rich uncle named you as the beneficiary of his life insurance policy.
The insurance company gives
you a choice of $100,000 today or a 12-year annuity of $12,000 at the end of each year.
What rate of
return is the insurance company offering?
Assume that you just inherited an annuity that will pay you $10,000 per year for 10 years, with the first
payment being made today.
A friend of your mother offers to give you $60,000 for the annuity.
If you
sell it to him, what rate of return will your mother’s friend earn on the investment?

SECTION 4-12
SOLUTIONS TO SELF-TEST
Interest rate
6%
Year
0
1
2
3
4
5
Ann Pmt
$0
$100
$100
$100
$100
$100
Lump Sum
$500
Total CFs
$0
$100
$100
$100
$100
$600
NPV
$794.87
Interest rate
6%
Year
0
1
2
3
4
5
6
7
8
9
Ann Pmt
$0
$100
$100
$100
$100
$100
$100
$100
$100
$100
Lump Sum
Total CFs
$0
$100
$100
$100
$100
$100
$100
$100
$100
$100
NPV
$1,015.21
Interest rate
8%
Year
0
1
2
3
4
CFs
$0
$100
$200
$0
$400
NPV
$558.07
What is the present value of a 5-year ordinary annuity of $100 plus an additional $500 at the end of
Year 5 if the interest rate is 6%?
How would the PV change if the $100 payments occurred in Years 1 through 10 and the $500 came at
the end of Year 10?
What is the present value of the following uneven cash flow stream:
$0 at Time 0, $100 at the end of
Year 1 (or at Time 1), $200 at the end of Year 2, $0 at the end of Year 3, and $400 at the end of Year 4,
assuming the interest rate is 8%?

10
$100
$500
$600

SECTION 4-13
SOLUTIONS TO SELF-TEST
Interest rate
15%
Year
0
1
2
3
CFs
$0
$100
$150
$300
FV of CFs
$0.00
$132.25
$172.50
$300.00
NFV
$604.75
What is the future value of this cash flow stream: $100 at the end of 1 year, $150 after 2 years, and
$300 after 3 years, assuming the appropriate interest rate is 15%?