Question

A weekly magazine offers a 1-year subscription for $45 and a 3-year subscription for $118. If you read the magazine for at least the next 6 years, which type of subscription would you prefer if the interest rate is 10% over the next 6 years? Assume the subscription rate remains the same over the next 6 years.

Answer 1

Alternative 1 : 1- Year Subscription for 6 Years

Outflow = $45 at the beginning of each year.
Interest Rate = 10%
We assume these funds to be borrowed at 10%.

FV of Outflow = ΣOutflow *(1+r)n
where r = interest rate
and n = no of years

FV of Outflow = [45 * (1.10)6] + [45 * (1.10)5] + [45 * (1.10)4] + [45 * (1.10)3] + [45 * (1.10)2] + [45 * (1.10)1]
                                    = 79.72 + 72.47 + 65.88 + 59.90 + 54.45 + 49.50
                            = $381.92

Alternative 2 : 3- Year Subscription for 2 times i.e upto 6 years

Outflow = $118 at the beginning of year 1 and year 4.
Interest Rate = 10%
We assume these funds to be borrowed at 10%.

FV of Outflow = ΣOutflow *(1+r)n
where r = interest rate
and n = no of years

FV of Outflow = [118 * (1.10)6] + [118 * (1.10)3]

                                    = 209.04 + 157.06
                            = $366.1

Since Alternate 2 has lower cash outflow it is better than Alternate 1 and hence 3 year subscription is better.