A telecommunication service provider is offering two payment options for its one-year unlimited talk mobile phone plan. pay the regular monthly subscription the end of each month for the next 12 months. Pay for the entire year in one lump sum at the beginning of the year. This amount be equal to 11 times the regular monthly subscription. If a subscriber’s MARR, expressed as an annual nominal interest rate compounded monthly, is 18%, should he choose Option 1 or Option 1?

## Expert Answer

Let’s compare both the options by calculating the present value of option 1.

As the payment is made at the end of each month, we can use formula for present value of ordinary annuity.

PV = C x [1- (1 + i)^{‑n} /i]

Where,

C = Payment amount

n = number of periods = 12

i = interest rate = 18 % p.a. = 0.18/12 = 0.015 p.m.

PV = C x [{1-(1+0.015)^{-12}} / 0.015]

= C x [{1-(1.015)^{-12}} / 0.015]

= C x [(1- 0.836387) / 0.015]

= C x (0.163613/ 0.015)

= C x 10.90751

For single payment we need to pay 11 times of regular payment amount.

Difference in payment amount = C x 11 – C x 10.90751

= C x 0.092494793

= C x 9.25%

Hence if we opt for lump sum payment at the beginning of the year, we have to pay 9.25 % extra amount.

Hence option 1 should be chosen.