Question

The present value of a series of payments of $3 at the end of every eight years, forever, is
equal to $9.5. Calculate the effective annual rate of interest.

Answer 1

$$\nu=\dfrac{1}{1+i}$$

$$PV=3\cdot\nu^8 +3\cdot\nu^{16}+...=\dfrac{3\cdot \nu^8}{1-\nu^8 }=9.5$$

$$\nu^8=\dfrac{9.5}{12.5}=0.76$$

$$\dfrac{1}{1+i}=\sqrt[8]{0.76}$$

$$i=\dfrac{1}{\sqrt[8]{0.76}}-1\approx0.0349$$

$$i=3.49\%$$