SOA Exam FM Sample Question 259
Study guide: Exam FM-2
At the end of each year for 60 years, Marilyn makes a deposit to a bank account that credits interest at an annual effective interest rate of i. She deposits 2 at the end of the first year, and each subsequent year her deposit increases by 2. At the end of 60 years, Marilyn uses the accumulated amount to purchase a 5-year annuity-immediate paying annually at the same annual interest rate of i, with a first payment of X and each subsequent payment increasing by 5%.
Which of the following expressions represents a correct equation of value?
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I.
\dfrac{2\left(s_{\overline{60}|}-60\right)}{i} = \dfrac{X\left(1-(1.05v)^5\right)}{i-0.05} -
II.
2(Ia)_{\overline{60}|} = Xv^{60}\left(1+1.05v+\ldots+(1.05v)^4\right) -
III.
2\displaystyle\sum_{t=0}^{59}s_{\overline{60-t}|} = X\left(v+1.05v^2+\ldots+1.05^4v^5\right) -
A) I only
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B) II only
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C) III only
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D) I, II, and III
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E) The correct answer is not given by (A), (B), (C), or (D).
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