SOA Exam FM Sample Question 293

Study guide: Exam FM-2

The present value of cash flows at an effective interest rate of $i$ is given by the following function:

$P(i) = 100 + 500(1+i)^{-3} - 1000(1+i)^{-4}, \text{ for } i > 0.$

Determine which of the following expressions represents the modified duration of these cash flows.

A) $\dfrac{1500(1+i)^{-4} - 4000(1+i)^{-5}}{100 + 500(1+i)^{-3} - 1000(1+i)^{-4}}$
B) $\dfrac{1500(1+i)^{-3} - 4000(1+i)^{-4}}{100 + 500(1+i)^{-3} - 1000(1+i)^{-4}}$
C) $\dfrac{-1500(1+i)^{-4} + 4000(1+i)^{-5}}{100 + 500(1+i)^{-3} - 1000(1+i)^{-4}}$
D) $\dfrac{-1500(1+i)^{-3} + 4000(1+i)^{-4}}{100 + 500(1+i)^{-3} - 1000(1+i)^{-4}}$
E) $\dfrac{-6000(1+i)^{-5} + 20{,}000(1+i)^{-6}}{100 + 500(1+i)^{-3} - 1000(1+i)^{-4}}$

Concepts tested