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?

  • $\begingroup$ Is this an actuarial science (exam FM) question? $\endgroup$ 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? $\endgroup$ Jan 29 '16 at 2:26
  • $\begingroup$ Mathematical Finance class $\endgroup$
    – user270494
    Jan 29 '16 at 2:28

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.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.