What is the effective interest rate for an investment fund that pays 6% interest compounded semiannually?
The effective interest rate for an investment fund that pays 6% interest compounded semiannually is 6.09%. The correct option is A. 6.09%.
To calculate the effective interest rate for an investment fund that pays 6% interest compounded semiannually, you can use the formula:
Effective interest rate = (1 + (interest rate / number of compounding periods))^number of compounding periods - 1
In this case, the interest rate is 6% (or 0.06 in decimal form) and the compounding periods are semiannually, which means they occur twice a year. Let's calculate it step by step:
Calculation
Given:
Interest rate = 6% = 0.06
Number of compounding periods = 2
Plugging the values into the formula:
Effective interest rate = (1 + (0.06 / 2))^2 - 1
Effective interest rate = (1 + 0.03)^2 - 1
Effective interest rate = (1.03)^2 - 1
Effective interest rate = 1.0609 - 1
Effective interest rate = 0.0609
Converting the decimal to percentage:
Effective interest rate = 6.09%
Therefore, the effective interest rate for an investment fund that pays 6% interest compounded semiannually is 6.09%. The correct answer is A. 6.09%.
Explanation:
Effective Interest Rate Formula:
The effective interest rate is a measure of the true return on investment after considering the effects of compounding. It reflects the total interest paid over a period as a percentage of the initial investment amount. The formula to calculate the effective interest rate is:
Effective interest rate = (1 + (interest rate / number of compounding periods))^number of compounding periods - 1
Given Data:
Interest rate = 6% = 0.06
Compounding periods = semiannually = 2 times a year
Calculation:
Plugging in the values:
Effective interest rate = (1 + (0.06 / 2))^2 - 1
Effective interest rate = (1 + 0.03)^2 - 1
Effective interest rate = (1.03)^2 - 1
Effective interest rate = 1.0609 - 1
Effective interest rate = 0.0609 = 6.09%
Therefore, the effective interest rate for an investment fund that pays 6% interest compounded semiannually is 6.09%. This means that if you invest in this fund, you will earn an effective interest rate of 6.09% annually due to the compounding effect. It is important to consider the effective interest rate when making investment decisions to understand the true return on your investment.