$1 is compounded semiannually for 10 years at 8% interest. What is the interest rate per period?
A. 4%
B. 2%
C. 8%
D. 1%
Answer (2)
Determine the number of compounding periods per year: Semiannually means twice a year.
Calculate the interest rate per period by dividing the annual interest rate by the number of compounding periods per year: 2 8% = 4% .
The interest rate per period is 4% .
Explanation
Understanding the Problem We are given that $1 is compounded semiannually for 10 years at 8% interest. We need to find the interest rate per period.
Finding the Interest Rate per Period Since the interest is compounded semiannually, this means that the interest is compounded twice per year. To find the interest rate per period, we need to divide the annual interest rate by the number of compounding periods per year.
Calculating the Interest Rate The annual interest rate is 8%, which can be written as 0.08. Since the interest is compounded semiannually, the number of compounding periods per year is 2. Therefore, the interest rate per period is 2 0.08 = 0.04 .
Expressing as Percentage To express the interest rate per period as a percentage, we multiply by 100: 0.04 × 100 = 4% . Therefore, the interest rate per period is 4%.
Final Answer The interest rate per period is 4%.
Examples
Understanding interest rates per period is crucial in personal finance. For instance, when comparing different loan options, knowing the interest rate per period helps you calculate the actual cost of borrowing. If you're considering a car loan with a 6% annual interest rate compounded monthly, the interest rate per period is 0.5%. This allows you to accurately determine your monthly payments and the total interest paid over the loan's duration, aiding in making informed financial decisions.
The interest rate per period for $1 compounded semiannually at 8% interest is 4%. This is calculated by dividing the annual interest rate by the number of compounding periods per year. Therefore, the answer is (A) 4%.
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