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Ethel and Jack each separately apply for and receive a loan worth $7,725 apiece. Ethel has a relatively average credit rating, so her loan has an APR of 9.14%, compounded monthly. Jack’s credit rating is excellent, so his loan has an APR of 6.88%, compounded monthly. If they both pay off their respective loans by making six years of identical monthly payments, how much more will Ethel pay than Jack?

Respuesta :

babbybratt17

Answer:

the answer is D. 613.44

Step-by-step explanation:

D..............

mickymike92

Based on amortization formula, Ethel will pay higher than Jack by $613.44

How much will each person pay?

The amount each is to pay for is calculated using the amortization formula:

  • P = a ÷ {{[(1 + r/n)^nt] - 1} ÷ [r/n(1 + r/n)^nt]}

where

  • P is monthly payment
  • a is credit amount
  • r is the interest rate
  • t is the time in years
  • n is number of times the interest is compounded

Amount paid by Ethel:

  • a = $7725
  • r = 9.14% = 0.0914
  • t = 6 years
  • n 12

P = a ÷ {{[(1 + r/n)^nt] - 1} ÷ [r/n(1 + r/n)^nt]}

P = $7725 ÷ {{[(1 + 0.0914/12)^12×6] - 1} ÷ [0.0914/12(1 + 0.0914/12)^12×6]}

P = $139.78

Total amount paid = $139.78 × 12 × 6 = $10,064.16

Amount paid by Jack:

  • a = $7725
  • r = 6.88% = 0.0688
  • t = 6 years
  • n = 12

P = a ÷ {{[(1 + r/n)^nt] - 1} ÷ [r/n(1 + r/n)^nt]}

P = $7725 ÷ {{[(1 + 0.0688/12)^12×6] - 1} ÷ [0.0688/12(1 + 0.0688/12)^12×6]}

P = $131.26

Total amount paid = $131.26 × 12 × 6 = $9,450.72

Difference in the amount Ethel and Jack will pay is = $10,064.16 - $9,450.72 = $613.44

Therefore, Ethel will pay higher than Jack by $613.44

Learn more about amortization at: https://brainly.com/question/24576997

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