The effective annual rate (EAR) for a loan with a stated APR of 10% compounded quarterly is closest to:a.9.65%.b.12.50%.c.15.00%d.10.00%.e.10.38%
Question
The effective annual rate (EAR) for a loan with a stated APR of 10% compounded quarterly is closest to:
a. 9.65%
b. 12.50%
c. 15.00%
d. 10.00%
e. 10.38%
Solution
The correct answer is e. 10.38%.
Here's the step-by-step calculation:
- The formula for the effective annual rate (EAR) when interest is compounded quarterly 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.
- In this case, r = 10% or 0.10, n = 4 (since interest is compounded quarterly), and t = 1 (since we're looking for the annual rate).
- Plugging
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