Question

How can I solve this using the HP 10bii financial calculator? A well-known financial writer argues that he can earn an extremely high return buying wine by the case. Specifically, he assumes that he will consume one $14 bottle of fine Bordeaux per week for the next 12 weeks. He can either pay $14 per week or buy a case of 12 bottles today. If he buys the case, he receives a discount of 8 percent. Assume he buys the wine and consumes the first bottle today. What is the EAR of purchasing wine by the case with this discount?

Answer 1

He can either pay $14 per week for 12 weeks

Or buy a case of 12 bottles today; suppose buying a case of 12 bottles today

Price of a case = 12 bottles * price of one bottle = 12 *$14 = $168

If he buys the case, he receives a discount of 8 percent

Therefore, Price of a case after discount = $168/ (1+8%) = $155.56

Now to calculate the effective annual rate (EAR); Price of a case after discount is the present value (PV), payment of $14 per week is PMT and 12 weeks are time period (n)

We can use formula of the present value (PV) of annuity due calculation as payment is beginning of the week

PV = PMT * [1- (1+i) ^-n / i] * (1+i)

Where,

Present value PV = $155.56

Weekly payments PMT = $14

Interest rate I/Y =?

Time period n = 12 weeks

Therefore,

$155.56 = $14 * [1- (1+i) ^-12 / i] * (1+i)

Or i = 1.43% per week

For weekly payment, effective annual rate (EAR) = (1 + r/m) ^m – 1

Where,

Effective annual rate (EAR) =?

Weekly rate r =1.43%

Period m = 52 weeks in a year (assumed)

Therefore,

EAR= (1 + 1.43%) ^52 - 1

Or EAR = 1.0939 or 109.39%

For financial calculator to calculate interest rate (I/Y)–

Changed to Begin Mode, Press CPT - PMT as payment is beginning of the week

Inputs are:

• PV = - $155.56 (type - 155.56 and then press PV)
• N= 12 (type 12 and then press N)
• PMT = $14 (type 14 and press PMT)
• FV = 0 (type 0 and press FV)

Now press I/Y to get the weekly interest rate then convert it in Effective annual rate (EAR) as mentioned above.