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Calculate the interest rate when the effective rate is \( 15 \% \) for each situation a. Compounded annually. b. Compounded semiannually. c. Compounded quarterly. d. Compounded monthly. c. Compounded

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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

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