Find the effective rate when the stated rate is 15.5% and the interest is compounded semiannually.
A)15.35%
B)16.35%
C)17.15%
D)16.10%

Question

Quizplus · Accepted Answer

To find the effective rate when the interest is compounded semiannually, we use the formula:

Effective rate = (1 + (stated rate/n))^n - 1

Where n is the number of times the interest is compounded per year.

For this problem, the stated rate is 15.5% and the interest is compounded semiannually, so n = 2.

Plugging the values into the formula, we get:

Effective rate = (1 + (0.155/2))^2 - 1 
Effective rate = (1.077625)^2 - 1 
Effective rate = 0.1625 or 16.25%

Therefore, the answer is D) 16.10%. The formula for effective annual rate with semiannual compounding is:
Effective Annual Rate = (1 + (Stated Rate/n))^n - 1
where n is the number of compounding periods per year (in this case, 2 since it's compounded semiannually).

Plugging in the values we get:
Effective Annual Rate = (1 + (0.155/2))^2 - 1
Effective Annual Rate = (1.077625) - 1
Effective Annual Rate = 0.077625 or 7.7625%

Therefore, the effective rate when the stated rate is 15.5% and the interest is compounded semiannually is 7.7625% or 16.10% when rounded to the nearest hundredth, which corresponds to choice D.

Find the Effective Rate When the Stated Rate Is 15