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A passbook savings account has a rate of 5%. Find the effective annual​ yield, rounded to the nearest tenth of a​ percent, if the interest is compounded semiannually.

User Vivid
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1 Answer

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Answer: 5.1%

Explanation:

The formula for calculating the effective annual yield when the interest is compounded semiannually is given by:

(1 + (r/n))^n - 1

where r is the annual interest rate and n is the number of times the interest is compounded in a year.

In this case, r = 5% and n = 2 (since the interest is compounded semiannually). Substituting these values into the formula, we get:

(1 + (0.05/2))^2 - 1

= (1.025)^2 - 1

= 1.050625 - 1

= 0.050625

Multiplying this value by 100 gives the effective annual yield as a percentage:

0.050625 x 100 = 5.0625%

Rounding this to the nearest tenth of a percent, we get:

Effective annual yield = 5.1%

Therefore, the effective annual yield for the given savings account, rounded to the nearest tenth of a percent, is 5.1%.

User Joshua Cheek
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