SOA Exam FM Sample Question 379
Study guide: Exam FM-2
An investor deposits 50,000 into a new savings account, which earns an annual effective discount rate of 3.2%. The investor then withdraws an amount X at the end of every two-year period. The balance at the end of 12 years, just after the withdrawal, is 45,000.
Determine which of the following is an equation of value that can be used to solve for X.
- A)
\dfrac{45{,}000}{(1.032)^{12}} + X\displaystyle\sum_{k=1}^{7}\dfrac{1}{(1.032)^{2(k-1)}} = 50{,}000 - B)
\dfrac{45{,}000}{(1.032)^{12}} + X\displaystyle\sum_{k=1}^{6}\dfrac{1}{(1.032)^{2k}} = 50{,}000 - C)
45{,}000(0.968)^{12} + X\displaystyle\sum_{k=1}^{6}(0.968)^{2k} = 50{,}000 - D)
\dfrac{45{,}000}{(1.032)^{12}} + X\displaystyle\sum_{k=1}^{6}(0.968)^{2k} = 50{,}000 - E)
45{,}000(0.968)^{12} + X\displaystyle\sum_{k=1}^{6}\dfrac{1}{(1.032)^{2k}} = 50{,}000
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