Question FM 11/13/2011 8:43

a) Find the accumulated value of $\$1$ at the end of n periods where the effective rate of interest for the k th period, k=1,2,...n, is defined by
$i_{k}=(1+r)^{k^{2}}(1+i)-1$
b)Show that the answer to a) can be written in the form $(1+j)^{n}$. Find j.

Ans:
a) $a(n)=(1+r)^{\frac{1}{6}(n)(n+1)(2n+1)}(1+i)^{n}$
b) $j=(1+r)^{\frac{1}{6}(n+1)(2n+1)}(1+i)-1$