What amount can be paid at the end of every month in perpetuity from an endowment of $350,000 which is earning 5.4% compounded monthly?

Question

What amount can be paid at the end of every month in perpetuity from an endowment of $350,000 which is earning 5.4% compounded monthly?

Am trying to apply the compound interest formula but it isn't working

Answer 1

It seems that the amount can not be more than the monthly earning of $$ m = 350000 \cdot 5.4/100 = 18900 $$ Otherwise the generating sum would shrink month by month and vanish within finite time.

I would also assume that the monthly payment is assumed to stay the same every month. Otherwise the problem is probably not uniquely solvable.

Answer 2

The present value of the sum of a monthly paid annuity ($a$) after $n$ years is

$PV=a\cdot \frac{(1+0.054/12)^n-1}{0.054/12}\cdot \frac{1}{(1+0.054/12)^n}$

Let $n$ go to infinity

$\lim_{n \to \infty}PV=\frac{a}{\frac{0.054}{12}}=a\cdot222.222$

Thus the equation is $350,000=a\cdot222.222$

$a=1575$