The effective annual rate (EAR) for a savings account with a stated APR of 4% compounded daily (use 365-day year) is closest to: a. 14.60%. b. none of them. c. 4.08%. d. 4.00%. e. 3.92%.
Question
The effective annual rate (EAR) for a savings account with a stated APR of 4% compounded daily (use 365-day year) is closest to:
a. 14.60%.
b. none of them.
c. 4.08%.
d. 4.00%.
e. 3.92%.
Solution
The correct answer is c. 4.08%.
Here's the step-by-step calculation:
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The formula for the effective annual rate (EAR) when interest is compounded daily is EAR = (1 + r/n)^(nt) - 1, where r is the annual interest rate (in decimal form), n is the number of compounding periods per year, and t is the number of years.
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In this case, r = 4% = 0.04, n = 365 (since interest is compounded daily), and t = 1 (since we're looking for the annual rate).
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Plugging these values into the formula gives EAR = (1 + 0.04/365)^(365*1) - 1 = 0.0408 or 4.08%.
Therefore, the effective annual rate for a savings account with a stated APR of 4% compounded daily is approximately 4.08%.
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