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On October 29, URXL Fitness Center signed a 200-day promissory note to purchase new workout equipment. The...

28. On October 29, URXL Fitness Center signed a 200-day promissory note to purchase new workout equipment. The note is worth $45,600 and is compounded annually at a rate of 6%. The fitness center made 2 partial payments on the note:
$12,000 on November 21
$9,500 on December 19
Find the new amount that is due at maturity.
○ $24,100.00
○ $25,039.16
○ $24,432.42
○ $33,774.80

Answer

To find the new amount due at maturity, we need to calculate the interest on the note and adjust for the partial payments.

  1. Calculate the interest on the original note for 200 days:

    2. Interest = Principal × Rate × Time = $45,600 × 0.06 × (200/365) = $1,497.53

  2. Add the interest to the original principal:

    3. Total amount = $45,600 + $1,497.53 = $47,097.53

  3. Calculate the interest on the first payment of $12,000 from November 21 to maturity:

    4. Time from November 21 to maturity = 200 - 23 = 177 days

    Interest on $12,000 = $12,000 × 0.06 × (177/365) = $348.49

  4. Calculate the interest on the second payment of $9,500 from December 19 to maturity:

    5. Time from December 19 to maturity = 200 - 51 = 149 days

    Interest on $9,500 = $9,500 × 0.06 × (149/365) = $232.11

  5. Subtract the payments and their respective interests from the total amount:

    6. New amount = $47,097.53 - ($12,000 + $348.49) - ($9,500 + $232.11) = $25,039.16

The new amount that is due at maturity is $25,039.16.

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