Answer:
To calculate the interest rate for different compounding periods when the effective rate is given, we can use the formula for compound interest:
�=�×(1+�/�)(�×�)A=P×(1+r/n)(n×t)
Where: A is the final amount or balance, P is the principal amount (initial investment), r is the interest rate (unknown in this case), n is the number of compounding periods per year, and t is the number of years.
Let's calculate the interest rate for each situation:
a. Compounded Annually: In this case, there is one compounding period per year.
�=�×(1+�/1)(1×�)A=P×(1+r/1). Compounded Semiannually: Here, we have two compounding periods per year.
�=�×(1+�/2)(2×�)A=P×(1+r/2)(2×t) �/�=(1+�/2)(2�)A/P=(1+r/2)(2t) (1+r/2)(2�)=�/�(1