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18 February, 06:24

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

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  1. 18 February, 06:40
    0
    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
  2. 18 February, 06:42
    0
    The EMR implied in Offer 1 is 16.51%.

    The EMR implied in Offer 2 is 0%.

    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%.
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