Question

A perpetuity pays $x at the end of each month. The nominal annual rate of interest compounded monthly is i
(12). Calculate the percentage of increase in the value of this perpetuity
if the nominal annual rate of interest compounded monthly decreases by 10%.

Answer 1

At the rate$i^{12}$ the present value of the perpetuity is;

$\frac{x}{i^(12)}$

A the rate $i^{(12)}(0.9)$ the present value of the perpetuity is;

$\frac{x}{i^(12)(0.9)}$

percentage increase in the value of perpetuity is found as;

$\frac{\frac{x}{i^(12)(0.9)}-\frac{x}{i^(12)}}{\frac{x}{i^(12)}}=\frac{1}{0.9}-1$

$=11.11111111$%