STT 455 Extra Credit Assignment
Problem 1
I have provided an electronic version of the illustrative life table in Microsoft Excel. You
are to reproduce all of the calculations for a life aged 50. That is, calculate:
1000 1000 1000 1000 1000 1000
Do NOT use the annuity-insurance relationship. You should only use the ages, , and
an interest rate for all calculations. You need to use these three base-values because
the other values provided in the table are rounded calculations that have previously
used these values.
In addition, calculate : | ( ) assuming a uniform. distribution of deaths between integer
ages. (Remember – because you can’t use the annuity-insurance relationship, you will
be unable to use ( ) and ( ) and will have to calculate this by interpolating the
probabilities. Also, ( ) and ( ) are rounded as well and you would need to
calculate these directly to have further accuracy even if you did want to use them).
Problem 2
A standard ultimate survival model follows Makeham’s Law as:
= + = 0.0003, =2.5×10%&, = 1.125, 0 ≤ ( ≤ ∞
For a standard select survival model, you are given:
• The select period is two years
• The ultimate part of the model is described as above
• The select part of the model follows:
* +,- = 0.85 %- ,- /01 0 ≤ 2 ≤ 2
Assume that the annual effective rate of interest is 3 = 0.05.
The model is an exponential-type model and technically has a nonfinite 4, but you may
assume that 4 = 120.
Part A
Use a radix of = 100,000. Create a life table
table below:
Format the cells as shown in the table and include the appropriate borders and stylings
(subscripts and superscripts, italics, etc.). Do NOT use the ROUND() function.
your table for x-values [20, 80], though you may need to extend these values to
beyond for calculation purposes.
Part B
Create a table of annuity and insurance
Format the cells as shown in the table and include the appropriate borders and stylings
(subscripts and superscripts, italics, etc.). Do NOT use the ROUND() function. Display
your table for x-values [20, 80], though you may need to extend these values to 120 and
beyond for calculation purposes.
containing the values shown in the
-type values shown in the table below:
Display
120 and
Problem 3
Assuming a constant force of mortality
3 =0.05, calculate the value of a linearly
initial payment of $1 on (() in three different ways:
1. By direct definition of (5
2. By using the relationship derived in the notes between
3. By deriving, yourself, a closed
This means no summation / integration / product
For these calculations, we will estimate the value.
calculation to four decimal places.
Problem 4
Produce the reserving schedule for a 10
end of the year of death for a life aged
illustrative life table. Here is a sample of the table:
When calculating the premium for the policy,
1. By using the assurance and annuity values directly from the table
2. By using techniques developed from the scheduling method
After you have calculated the premium in both ways, produce the reserving schedules
using those premiums. Notice the effect of accuracy and rounding.
For your tables, there will be a lot of digits, so it may be easier to work in other units
than raw dollars (such as millions) for the sake of reading and displaying purposes.
(() =0.02 and an annual effective interest rate
-increasing whole life insurance policy with an
)
(5 ) and
-form. formula
–type operators.
̅ = 789/((+:);: = +<
Use 300 terms and round your
-year term insurance that pays $5
66. Assume that mortality and interest follow the
you will calculate this in two ways:
For example,
0,000 at the
To be submitted
You will submit a Microsoft Excel file to D2L. Please format the file name as:
Last_name, First_name – STT 455 FS17 – Extra Credit
This assignment is worth a GPA increase of 0.5 points. You must get every question
100% correct in order to receive this increase. In other words, it is all-or-nothing!
Good luck!