Problem 1: Sylvio is turning 60 and plans to retire early at the end of the year. He will start receiving his pension when he turns 67, i.e., in 7 years. He has some saving and plans to invest in bonds to graduate a stream of income for the next 6 years (age 61 through 66). Specifically, he aims at starting at $56,000 next year and then each year receiving $2,000 less than the previous year, ending up with $46,000 when he is 66. Sylvio can invest in a number of bonds, all of which have face value $1,000, described as follows:
|
Bonds
|
Coupon Rate (%)
|
Maturity
|
Price
|
|
A
|
4
|
6 years
|
$977.19
|
|
B
|
2
|
6 years
|
$872.54
|
|
C
|
0
|
5 years
|
$812.12
|
|
D
|
0
|
4 years
|
$854.80
|
|
E
|
0
|
3 years
|
$895.44
|
|
F
|
8
|
2 years
|
$1,085.67
|
|
G
|
0
|
1 years
|
$968.52
|
All coupons payments are annual and, therefore, you should use annual compounding throughout. His current savings are $275,000. In addition to guaranteeing the cash flow stream described above, Sylvio wants to receive a single payment at the end of year 3 which he plans to spend on a cruise to celebrate his 30th wedding anniversary.
a. How many units of each bond does Sylvio need to buy or sell?
b. How much will Sylvio get to spend on the cruise?