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I'm having trouble with two questions

  1. A fund earns a nominal rate of interest of 6% compounded every two years. Calculate the amount that must be contributed now to have 1000 at the end of six years.

My thoughts:

Since it is compounded every two years, then the interest is divided by $.5$, so I get:

$Present Value = 1000*1/(1+2*0.06)^3$ = $711.78$

Is that correct?

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  • $\begingroup$ Is this an actuarial science (exam FM) question? $\endgroup$ – Clarinetist Jan 29 '16 at 2:22
  • $\begingroup$ @Clarinetist No, a textbook question I'm trying to figure out $\endgroup$ – user270494 Jan 29 '16 at 2:25
  • $\begingroup$ Could you give more context? What textbook is this? Is this in a finance class, math class, or actuarial science class? $\endgroup$ – Clarinetist Jan 29 '16 at 2:26
  • $\begingroup$ Mathematical Finance class $\endgroup$ – user270494 Jan 29 '16 at 2:28
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Your answer is correct.

This answer assumes that you know actuarial notation. Judging by your previous questions, you do. We have $$i^{(1/2)} = 0.06$$ (why?), and thus the effective rate is $$\dfrac{i^{(1/2)}}{1/2} = 0.12\text{.}$$ This is the two-year effective rate. Six years is equivalent to three two-year periods. The equivalent discount factor is $$v = \dfrac{1}{1.12}$$ so the present value of $1000$ from three two-year periods is $$1000v^{3} = \dfrac{1000}{(1.12)^3}$$ which matches your answer.

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