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Text Box: A Special Shortcut for Some Force of Interest Accumulation Problems Sometimes a certain type of problem shows up so often on actuarial exams that it makes knowing a shortcut for the problem worthwhile. Such is the case with this week’s tip, which involves computing the accumulation function when the force of interest is given in a certain form Generally, given the force of interest at time t, , then the accumulation function is . By evaluating the integral and using rules for logarithms and exponentials, we can derive the following often tested special case: Example: Suppose , . Billie Joe deposits 5 at time 0 and X at time 6. The accumulated value in her account at time 9 is 30. Determine X. Solution: Notice that  where . Therefore, by the above formula, . So the accumulated value at time 9 of the deposit of 5 at time 0 is , and the accumulated value at time 9 of the deposit of X at time 6 is . We get .