Question

A popular magazine offers a lifetime subscription for $1000. Such a subscription may be given as a gift to an infant at birth (the parents can read it in those early years), or taken out by an individual for himself. Normally, the magazine costs $64.50 per year. Knowledgeable people say it probably will continue indefinitely at this $64.50 rate. What is the rate of return on a life subscription purchased for an infant

Answer 1

Answer:

rate of return on lifetime subscription purchase is 6.89 %

Explanation:

given data

lifetime subscription = $1000

magazine costs = $64.50 per year

to find out

rate of return on a life subscription purchased

solution

we know that rate of return is obtain by  the equation

the present value $64.5 for infinite years to 1000

so

1000 = 64.5 + $\frac{64.5}{(1+i)}$ + $\frac{64.5}{(1+i)^2}$ + $\frac{64.5}{(1+i)^3}$ +  ................ ∞ + $\frac{64.5}{(1+i)^∞}$

and

r = $\frac{1}{(1+i)}$

so by using geometric series for the infinity term

1000 = $\frac{64.5}{(1-r)}$

r = 0.9355

so r = $\frac{1}{(1+i)}$

0.9355 = $\frac{1}{(1+i)}$

i = 6.89 %

so rate of return on lifetime subscription purchase is 6.89 %