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First Choice Bank wants to earn an effective interest rate of 18% per year. In order to suit different potential borrowers' needs, the bank offers two options. The first calculates interest on a weekly compounding basis while the second calculates interest on a monthly compounding basis. What interest rate is the bank required to report for the two options? Give one reason why a borrower might prefer monthly compounding over weekly compounding.

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Answer:

What interest rate is the bank required to report for the two options?

  • APR for weekly compounding = 0.003188 x 52 = 0.1658 = 16.58%
  • APR for monthly compounding = 0.01389 x 12 = 0.1667 = 16.67%

Give one reason why a borrower might prefer monthly compounding over weekly compounding.

  • In this case, the lender should be indifferent between monthly or weekly compounding since the effective interest rate is equal for both (if the pay in during the first week). But generally, borrowers should choose the longest compounding period option. The longer the compounding period, the less interests charged will earn more interest. In some cases. If you pay after the second week started, then you might be charged a slightly higher interest.

Explanation:

effective interest rate = (1 + i/n)ⁿ - 1

for weekly compounding:

0.18 = (1 + i)⁵² - 1

1.18 = (1 + i)⁵²

⁵²√1.18  = ⁵²√(1 + i)⁵²

1.003188 = 1 + i

0.003188 = i

for monthly compounding:

0.18 = (1 + i)¹² - 1

1.18 = (1 + i)¹²

¹²√1.18  = ¹²√(1 + i)¹²

1.01389 = 1 + i

0.01389 = i

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