Periodic interest rates. You have a savings account in which you leave the funds

Question

Periodic interest rates. You have a savings account in which you leave the funds for one year without adding to or withdrawing from the account. Which would you rather have: a daily compounded rate of 0.050%, a weekly compounded rate of 0.325%, a monthly compounded rate of 1.45%, a quarterly compounded rater of 3.75%, a semiannually compounded rate of 8%, or an annually compounded rate of 18%? What is the effective annual rate (EAR) of a daily compounded rate of 0.050%? % (Round to two decimal places.)

Explanation / Answer

Effective annual rate = EAR

R = Rate

N = Compounding frequency

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Formula for Effective annual rate:

EAR = (1 + R)^N -1

1.

N = Daily = 365

EAR = (1+0.05%)^365-1 = 20.02%

2.

N = Weekly = 52

EAR = (1+0.325%)^52 -1 = 18.38%

3.

N = Monthly = 12

EAR = (1+1.45%)^12 -1 = 18.86%

4.

N = Quarterly = 4

EAR = (1+3.75%)^4 -1 = 15.87%

5.

N = Semi-annually = 2

EAR = (1+8%)^2 -1 = 16.64%

6.

N = Annually = 1

EAR = (1+18%)^1 -1 = 18.00%

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One should go for daily compounding rate.

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