Spot Rates

[Gekko11]

Is there an easier way to calculate this using the BA II Plus calculator? This Question took me almost 4.5min to answer
Given the following forward rates, the value of a 4-year, 11% annual pay, $1,000 par bond, is closest to:
Year
Rate

1
7.00%

2
8.15%

3
10.30%

4
12.00%

Note that the year 1 rate is the current rate (or spot rate) on a 1-year security.
A) $1,052.63.

B) $984.25.

C) $1,060.36.

correct answer C) $1,060.36.
Spot Rates:
Year 1 = 7%.
Year 2 = [(1.07)(1.0815)]1/2 – 1 = 7.57%.
Year 3 = [(1.07)(1.0815)(1.103)]1/3 – 1 = 8.48%.
Year 4 = [(1.07)(1.0815)(1.103)(1.120)]1/4 – 1 = 9.35%.
Bond Value:
N = 1; FV = 110; I/Y = 7; CPT → PV = 102.80
N = 2; FV = 110; I/Y = 7.57; CPT → PV = 95.06
N = 3; FV = 110; I/Y = 8.48; CPT → PV = 86.17
N = 4; FV = 1,110; I/Y = 9.35; CPT → PV = 776.33
102.80 + 95.06 + 86.17 + 776.33 = 1,060.36

 

[pokhim]

Not sure…good question though.

 

[Wojtek]

Work the bond backwards:
Discount the Year 4 cash flow ($1,000 + $110) by one period using the Year 4 rate:
$1,100/1.12 = whatever result you get, add $110
Now, discount the total by the Year 3 rate, i.e. ((1,110/1.12) + 110)/1.103 = whatever result you get, add $110 … and so on.
Effectively, you are performing the following computation:
(((((((1,110/1.12) + 110)/1.103) + 110)/1.0815) + 110)/1.07)
You will arrive at the same bond value and it should take less than 1 minute.

 

[bloodline]

good one!!!!