Chapter 9.2, Problem 19E

To determine

(a)

To find:

The balance in the annuity after 10 years and the time at which the annuity runs out of funds.

To determine

(b)

To show:

a continuous annuity with given withdrawal rate and interest rate funded by an initial deposit never runs out of money.

To determine

(c)

To find:

The minimum initial deposits $P_0$ that will allow an annuity indefinitely.

To determine

(d)

To find:

The minimum initial deposits $P_0$ necessary to fund an annuity for 20 years.

To determine

(e)

To find:

The minimum rate of interest $r$ that the annuity must allow withdrawal to continue indefinitely.

To determine

(f)

To show:

a continuous annuity never returns outs of money if the initial balance is equal to or greater than $\frac{N}{r}$.