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James invests at 3.7% interest compounded quarterly. What is the effective annual yield?

a) 3.70%

b) 3.72%

c) 3.75%

d) 3.78%

1 Answer

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Final answer:

The effective annual yield for James's investment at 3.7% interest compounded quarterly is calculated using the formula for compound interest. The yield is approximately 3.74%, with the closest provided option being 3.75%.

Step-by-step explanation:

When James invests at 3.7% interest compounded quarterly, the effective annual yield can be calculated using the formula for compound interest. The formula to find the effective annual yield (EAY) is given by EAY = (1 + r/n)n - 1, where r is the annual interest rate and n is the number of compounding periods per year. In this case, the interest rate r is 3.7% or 0.037, and the number of compounding periods n is 4 (since interest is compounded quarterly).

Plugging these values into the formula gives us:

EAY = (1 + 0.037/4)4 - 1

EAY = (1 + 0.00925)4 - 1

EAY = 1.009254 - 1

EAY ≈ 1.0374 - 1

EAY ≈ 0.0374 or 3.74%

Therefore, the correct answer is not exactly listed among the options, but the closest one is (c) 3.75%.

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