SOA Exam FM Sample Question 36

Study guide: Exam FM-2

Happy and financially astute parents decide at the birth of their daughter that they will need to provide 50,000 at each of their daughter's 18th, 19th, 20th, and 21st birthdays to fund her college education. They plan to contribute $X$ at each of their daughter's 1st through 17th birthdays to fund the four 50,000 withdrawals. They anticipate earning a constant 5% annual effective interest rate on their contributions.

Let $v = 1/1.05$ .

Determine which of the following equations of value can be used to calculate $X$ .

A) $X\displaystyle\sum_{k=1}^{17} v^k = 50{,}000[v+v^2+v^3+v^4]$
B) $X\displaystyle\sum_{k=1}^{16} 1.05^k = 50{,}000[1+v+v^2+v^3]$
C) $X\displaystyle\sum_{k=0}^{17} 1.05^k = 50{,}000[1+v+v^2+v^3]$
D) $X\displaystyle\sum_{k=1}^{17} 1.05^k = 50{,}000[1+v+v^2+v^3]$
E) $X\displaystyle\sum_{k=0}^{17} v^k = 50{,}000[v^{18}+v^{19}+v^{20}+v^{21}+v^{22}]$

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SOA Exam FM Sample Question 36

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