what is the effective rate of $18,000 invested for one year at 8.0%,compounded semiannually?
To find the effective rate of interest on an investment compounded semiannually, you can use the formula:
Effective Rate = (1 + (Nominal Rate / Number of Compounding Periods))^Number of Compounding Periods - 1
In this case, the nominal rate is 8.0%, and the investment is compounded semiannually. Therefore, you need to calculate the effective rate for two compounding periods (one year).
Step 1: Convert the nominal rate to a decimal:
Nominal Rate = 8.0% = 8.0 / 100 = 0.08
Step 2: Calculate the effective rate using the formula:
Effective Rate = (1 + (0.08 / 2))^2 - 1
Simplifying the formula:
Effective Rate = (1 + 0.04)^2 - 1
Effective Rate = (1.04)^2 - 1
Effective Rate = 1.0816 - 1
Effective Rate = 0.0816
Step 3: Convert the effective rate to a percentage:
Effective Rate = 0.0816 x 100 = 8.16%
Therefore, the effective rate of $18,000 invested for one year at 8.0% compounded semiannually is approximately 8.16%.