Question

3. You want to buy a new refrigerator with a price tag of $3,000 and the seller has two special offers for you. Offer 1 (zero-interest financing): You make a down payment of $300 now and 36 consecutive monthly installments of $75 (the first payment is due in one month). Offer 2 (immediate cash back): You make a full payment now and get an immediate $400 cash back. The two offers cannot be combined with each other. What is the effective monthly interest rate (EMR) implied in these two offers

Answer 1

The EMR implied in Offer 1 is 16.51%.

The EMR implied in Offer 2 is 0%.

Step-by-step explanation:

Offer 1:

Price tag = $3,000

Purchase price = $3,000 - 400 = $2,600

Amount paid = $300 + ($75 × 36) = $300 + $2,700 = $3,000

Interest amount = Amount paid - Purchase price = $3,000 - $2,600 = 400.

Nominal interest rate = Interest amount/Purchase price = 400/2,600 = 0.1538, 15.38.

To calculate the EMR, we use the EMR formula as follows:

EMR = (1 + (i/n))^n - 1 ................................... (1)

Where;

i = nominal interest rate = 0.1538

n = number of compounding period per year = 12 months

Substitute the values into equation (1), we have:

EMR = (1 + (0.1538/12))^12 - 1 = 0.1651, or 16.51%

Therefore, the EMR implied in Offer 1 is 16.51%.

Offer 2:

Price tag = $3,000

Purchase price = $3,000 - 400 = $2,600

Amount paid = $3,000 - 400 = $2,600

Interest amount = Amount paid - Purchase price = $2,600 - $2,600 = 0.

Therefore, the EMR implied in Offer 2 is 0%.

Answer 2

Answer: the FIRST offer has zero EMR

the second offer has -13% EMR

Explanation:

The first offer has total amount of $300 + ($75x36) = $3000, this means there is no interest.

The second offer will have customer paying $3000 - $400 = $2600, there is a $400 reduction from the price.

$400 is 13% of #3000