A passbook savings account has a rate of 6.7 %. Find the effective annual yield if the interest is compounded semiannually.

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Accepted Answer

Step:1 ：Substitute the given values into the formula for effective annual yield (EAY): (EAY = (1 + frac{r}{n})^{nt} - 1), where (r = 0.067), (n = 2), and (t = 1)Step:2 ：Calculate the value inside the parentheses: ((1 + frac{0.067}{2})^2 - 1 = (1 + 0.0335)^2 - 1)Step:3 ：Calculate the exponent: (1.067^2 - 1 = 1.138489 - 1)Step:4 ：Subtract 1 from the result: (1.138489 - 1 = 0.138489)Step:5 ：The effective annual yield is approximately 13.85% when rounded to two decimal places: (boxed{0.138489})

Answer

Step: 1 ：Substitute the given values into the formula for effective annual yield (EAY): (EAY = (1 + frac{r}{n})^{nt} - 1), where (r = 0.067), (n = 2), and (t = 1)Step: 2 ：Calculate the value inside the parentheses: ((1 + frac{0.067}{2})^2 - 1 = (1 + 0.0335)^2 - 1)Step: 3 ：Calculate the exponent: (1.067^2 - 1 = 1.138489 - 1)Step: 4 ：Subtract 1 from the result: (1.138489 - 1 = 0.138489)Step: 5 ：The effective annual yield is approximately 13.85% when rounded to two decimal places: (boxed{0.138489})

A passbook savings account has a rate of $6.7 \%$. Find the effective annual yield if the interest is compounded semiannually.

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