 Method 1: 40000000/(a_{200.03125}) = $2,719,796.28 per half year.
Method 2: Each bond costs 1000+(4532.50)a_{200.0325} = $1181.74.
Selling the strip bond gives 1000(1.03)^{20} = $553.68. Thus the
net cost of each bond (coupons only) is 1181.74553.68 = $628.06. Let
n be the number that can be purchased. Then 628.06(n) = 40,000,000 so
n = 63688.183 or n = 63,688 bonds. Thus the coupons at $45 each bring in
(63688)(45) = $2,865,960.00 per half year.
Hence method 2 produces over $146,000 more revenue per half year than method 1.
 The price P_{0} on January 1, 2001 is, by Makeham's formula,
F_{0}+(0.04/0.03)(FF_{0}) where F_{0} = 1000000((1.03)^{17}+º+(1.03)^{29})
= 1000000(a_{290.03}a_{160.03}) = $6,627,352.56 and F = $13,000,000.
Hence P_{0} = $15,124,215.81. Finally on May 6, 2001 the price
P = P_{0}(1+(0.03)(1261)/(1821)) = $15,437,562.82.
 At 7% the NPV is 1,400,000+200,000a_{110.07}100,000(1.07)^{12}
=$55,333.67. Yes, at 7% this is a suitable investment.
At 8% the NPV is 1,400,000+200,000a_{110.08}100,000(1.08)^{12}
= $11,918.52. No, at 8% this is not a suitable investment.
We can estimate an IRR by doing linear interpolation between 7% and 8%.
Thus (i7)/(87) = (055333.67)/(11918.5255333.67) = 0.823. Thus
an IRR for this cash flow is 7.82%
 K_{A} = 125000 + (12500018000)/(1.07^{9}1) + 7900/0.07 = $365,472.18.
K_{B} = 175000 + (17500025000)/(1.07^{12}1) + 9200/0.07 = $426,218.55.
On a per ton basis: K_{A}/39 = $9371.08 and K_{B}/45 = $9471.52. Hence the
type A truck is more economical.
 Without the kit, K_{1} = 21000 + (210005000)/(1.06^{9}1) + 1000/0.06
= $60,872.60.
With a kit costing X, K_{2} = 21000+X + (21000+X5000)/(1.06^{12}1)
+ 500/0.06 = $45140.54 + 1.98795049X.
Let the number of units made per year without the kit be U. Then with the kit the
units made per year is 1.1U. Thus on a unit basis: K_{1}/U = K_{2}/(1.1U)
or 1.1K_{1} = K_{2}. Thus X = $10,975.79 is the amount one should be willing
to pay for the kit.

 R_{5} = (1/8)(350007000) = $3500.00.
 35000(1d)^{8} = 7000 so 1d = 0.8177654 and d = 0.182235. Thus
R_{5} = 35000(0.8177654)^{4}(0.182235) = $2852.43.
 New car price in 4 years = 36000(1.05) = $37800. Book value of
her car in 4 years = 36000(1d)^{4} where 36000(1d)^{10} = 4000.
Thus the book value in 4 years is 36000(4000/36000)^{4/10} = $14948.77.
She must save 37800.00  14948.77 = $22851.23 in 4 years (= 48 months).
Hence her monthly SF deposit should be 22851.23/s_{480.06/12} = $422.41.

 The probability a person aged 18 survives 20 years to reach age 38
is l_{38}/l_{18}. But this ratio depends on the mortality class: female
nonsmoker, female smoker, male nonsmoker, male smoker. Using the appropriate
table we get the four ratios (9871801/9956686) = 0.991474573,
(9828627/9955889) = 0.987217415, (9761201/9938575) = 0.982152975,
(9684598/9936586) = 0.974640385. The probability that all 25 students
survive 20 years is (0.991474573)^{5}(0.987217415)^{5}(0.982152975)^{7}(0.974640385)^{6} =
0.678879. Thus the probability that at least one dies by this time is
1  0.678879 = 0.3211.
 The probability a person aged 18 survives 80 years to reach age 98
is l_{98}/l_{18}. As above, there are four ratios for the 4 classes of
mortality. They are: 0.068030969, 0.041391984, 0.02035161, 0.009406551.
The probabilities of dying before age 98 are one minus these values or:
0.931969031, 0.958608016, 0.97964839, 0.990593449. The probability that
all 25 students die before age 98 is the product
(0.931969031)^{5}(0.958608016)^{5}(0.97964839)^{7}(0.990593449)^{6} = 0.4656686.
The probability that at least one survives is one minus this or 0.5343.
 If the payments are each R then the expected values of the payments
are R(0.99), R(0.99)^{2}, to R(0.99)^{48}. To find the present value of
these payments, introduce an interest rate i such that
(1+i) = (1+0.09/12)/0.99. Hence i = 0.017676768. Thus
10000 = Ra_{480.017676768} and R = $310.80 per month for 4 years.
 10000 = XD_{65}/D_{32} so X = 10000D_{32}/D_{65}.
a. Using the male smoker mortality table with i = 6% we get X = 90188.04. The
size of the endowment is $90,188.04.
b. From a bank he would get 10000(1.06)^{33} = $68,405.90.
c. Using the female nonsmoker tables at 6% gives and endowment of $74,874.14.