An investment grows at a force of interest $\delta(t)= \frac{3\sqrt{t}}{100}$. Calculate the effective annual rate of interest over $4$ years.
$a(t)=e^{\int_0^t \frac{3\sqrt{t}}{100} dt}=e^{\frac{2}{100}t^{\frac{3}{2}}}-1$
$a(4)=e^{\frac{4}{25}}-1$
The answer provided is $a(4)=e^{\frac{1}{25}}-1$
$\endgroup$1 Answer
$\begingroup$$a(4)=e^{\frac{4}{25}}$
$(1+i)^4=e^{\frac{4}{25}}$
Taking $ln$
$\rightarrow 4\ln{(1+i)}=\frac{4}{25}$
$\ln{1+i}=\frac{1}{25}$
$\therefore i=e^{\frac{1}{25}}-1$
$\endgroup$
