Question

At what rate of interest, convertible semiannually, is $10,000 the present value of $1,000 paid at the end of every half-year for 6 years?

Answer 1

Let the rate of interest be r % per annum.

$A=P(1+\frac r{2\times100})^{2n}$

$10000=1000(1+\frac r{200})^{12}$

$1+\frac{r}{200}=$ $10^{1/12}\approx 1.211$

r$\approx$ 42%.