Learning Center
How to calculate a life insurance premium?
A fair value of a life insurance premium corresponds to the discounted value of the value of the insurance that will be paid in case of death of the insured person multiplied by the chance of paying the life insurance at a given age. To illustrate how the Actuarial Toolbox handles with this subject, we will show the direct calculus of the premium via the function “sActuarialLifeInsurance” for insurance of $100,000 for a 40-year-old person. Just for the completeness of the explanation, we will also present the calculus using the chance of someone dying at the exact age times the value of the insurance.
For the direct calculus, simply select the Products/Assurance (liability) option at the Actuarial Toolbox tab and change the inputs accordingly. Let’s suppose that the table UP 1994 - Female is the relevant table to represent the mortality force that acts upon the insured person’s life. The results can be seen below:
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C |
1 |
Life insurance example (direct calculus) |
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2 |
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3 |
Forward (real) interest rate curve |
0.05 |
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4 |
Normal life table |
6 |
UP1994F |
5 |
Current age |
40 |
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6 |
Number of payments |
131 |
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7 |
Assurance value |
$ 100,000.00 |
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8 |
Annuity (present value) |
$ 13,699.36 |
=sActuarialAssuranceLiability(sActuarialFlatRateVector($B$3),$B$4,$B$5,$B$6)*$B$7 |
9 |
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The appropriate function for the indirect calculus is the “sActuarialqxnpxVector” that returns the desired probabilities. It can be inserted selecting the option Common operations/qxnpx (vector) at the Actuarial Toolbox tab. Also, the discounting factors can also be inserted through the option Financial/Discount factor (vector) available at the actuarial tab. Now, multiplying and summing the columns as presented in cell B7 (see below) gives the desired result.
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F |
G |
1 |
Life insurance example (indirect calculus) |
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2 |
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3 |
Actuarial table |
6 |
UP1994F |
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4 |
Age |
40 |
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5 |
Interest rate |
0.05 |
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6 |
Assurance value |
$ 100,000.00 |
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7 |
Annuity (present value) |
$ 13,699.36 |
=SUM(F50:F140) |
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8 |
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9 |
Age |
Probability of dying on the exact age |
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10 |
0 |
0 |
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11 |
1 |
0 |
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... |
... |
... |
... |
... |
... |
... |
... |
49 |
39 |
0 |
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Discount factors |
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50 |
40 |
0.000763 |
={sActuarialqxnpxVector($B$3,$B$4)} |
0.952380952 |
={sActuarialForwardInterestRatesToDiscountFactorForecastVector( sActuarialFlatRateVector($B$5))} |
72.66667 |
=B50*D50*$B$6 |
51 |
41 |
0.00082537 |
Note: after entering the above formula click on the "Multiple Values Formula" button. |
0.907029478 |
Note: after entering the above formula click on the "Multiple Values Formula" button. |
74.86347 |
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52 |
42 |
0.00088659 |
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0.863837599 |
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76.58694 |
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53 |
43 |
0.000940666 |
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0.822702475 |
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77.38883 |
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54 |
44 |
0.000988612 |
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0.783526166 |
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77.46031 |
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55 |
45 |
0.001041393 |
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0.746215397 |
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77.71036 |
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56 |
46 |
0.00110495 |
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0.71068133 |
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78.52673 |
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57 |
47 |
0.001188166 |
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0.676839362 |
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80.41972 |
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58 |
48 |
0.001286963 |
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0.644608916 |
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82.95877 |
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59 |
49 |
0.001395292 |
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0.613913254 |
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85.65881 |
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60 |
50 |
0.001519993 |
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0.584679289 |
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88.87086 |
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... |
... |
... |
... |
... |
... |
... |
... |
127 |
117 |
8.57297E-07 |
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0.022245116 |
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0.001907 |
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128 |
118 |
4.28649E-07 |
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0.021185825 |
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0.000908 |
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129 |
119 |
2.14324E-07 |
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0.020176976 |
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0.000432 |
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130 |
120 |
2.14324E-07 |
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0.019216167 |
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0.000412 |
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131 |
121 |
0 |
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0.018301112 |
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0 |
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132 |
122 |
0 |
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0.01742963 |
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0 |
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133 |
123 |
0 |
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0.016599648 |
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0 |
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134 |
124 |
0 |
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0.015809189 |
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0 |
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135 |
125 |
0 |
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0.01505637 |
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0 |
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136 |
126 |
0 |
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0.0143394 |
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0 |
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137 |
127 |
0 |
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0.013656571 |
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0 |
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138 |
128 |
0 |
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0.013006259 |
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0 |
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139 |
129 |
0 |
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0.012386913 |
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0 |
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140 |
130 |
0 |
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0.01179706 |
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0 |
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141 |
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