Assume you have Sirius XM in your car and pay Sirius each month END. You are off

Question

Assume you have Sirius XM in your car and pay Sirius each month END. You are offered the following deal:

1)  A two year contract (24 months) with payments fixed at $12/month (i.e. no increase in rate for two years), OR

2) Prepay two years worth of service equivalent to $12/month in exchange for a 10% discount equal to $28.80 ($12 x 24 = $288 x 10%). Thus you would pay $259.20 today ($288 x 90%) and save $12/month for two years.

Assume you have sufficient cash in the bank earning 10 basis points per year and have no concerns over the quality of service or Sirius financial future.

What is the implicit interest rate in this deal and should you prepay?

Explanation / Answer

Answer:

1. Implicit interest rate : Given: PV = 259.20, FV = 288, pmt -12 per month , nper 24, So if you apply PV formula to calcluate rate PV = FV/(1+r)^n. putting values in the formula we get 5% as an interest rate.

2. you should prepay since if you prepay it will cost you 10.8$/month however if you are paying on month on month basis then it would cost you more.

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