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

rate of return on lifetime subscription purchase is 6.89 %

Step-by-step 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 +
`(64.5)/((1+i))` +
`(64.5)/((1+i)^2)` +
`(64.5)/((1+i)^3)` + ................ ∞ +
`(64.5)/((1+i)^∞)`

and

r =
`(1)/((1+i))`

so by using geometric series for the infinity term

1000 =
`(64.5)/((1-r))`

r = 0.9355

so r =
`(1)/((1+i))`

0.9355 =
`(1)/((1+i))`

i = 6.89 %

so rate of return on lifetime subscription purchase is 6.89 %