Chapter 13.4, Problem 30E

To determine

(a)

To show:

To set up an annuity in perpetuity of amount $R$ per time period, the amount that must be invested now is

$A_p=\frac{R}{1+i}+\frac{R}{{\left(1+i\right)}^2}+\frac{R}{{\left(1+i\right)}^3}+\cdots +\frac{R}{{\left(1+i\right)}^n}+\cdots$

With the help of a timeline, where $i$ is the interest rate per time period.

To determine

(b)

To show:

The sum of the infinite series $A_p$, is given by

$A_p=\frac{R}{i}$

To determine

(c)

To find:

The money that must be invested now at $10\%peryear$, to provide an annuity in perpetuity of $\$5000peryear$.

To determine

(d)

To find:

The money that must be invested now at $8\%peryear$, compounded quarterly, to provide an annuity in perpetuity of $\$3000peryear$.