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In Mathematics / College | 2025-07-05

Find the total number of compounding periods and the interest rate per period for the investment.

| Term of Investment | Nominal (Annual) Rate (%) | Interest Compounded | Compounding Periods | Rate per Period (%) |
|---|---|---|---|---|
| 9 years | 4 | quarterly | | |

Asked by vc5jmwm974

Answer (2)

Calculate the total number of compounding periods: 9 × 4 = 36 .
Calculate the interest rate per period: 4 4 ​ = 1 .
The total number of compounding periods is 36.
The interest rate per period is 1%. 36 , 1 ​

Explanation

Understanding the Problem We are given an investment with a term of 9 years, a nominal annual interest rate of 4%, and interest compounded quarterly. We need to find the total number of compounding periods and the interest rate per period.

Calculating Compounding Periods To find the total number of compounding periods, we multiply the term of the investment (in years) by the number of times the interest is compounded per year. Since the interest is compounded quarterly, it is compounded 4 times per year. Thus, the total number of compounding periods is: 9 years × 4 year periods ​ = 36 periods

Calculating Interest Rate per Period To find the interest rate per period, we divide the nominal annual interest rate by the number of times the interest is compounded per year. The nominal annual interest rate is 4%, and the interest is compounded quarterly (4 times per year). Thus, the interest rate per period is: 4 4% ​ = 1%

Final Answer Therefore, the total number of compounding periods is 36, and the interest rate per period is 1%.


Examples
Understanding compounding periods and interest rates is crucial in personal finance. For instance, when planning for retirement, knowing how frequently your investments compound can significantly impact your long-term returns. Similarly, when taking out a loan, understanding the compounding frequency helps you assess the true cost of borrowing. By calculating these values, you can make informed decisions about savings, investments, and loans, ensuring you're financially prepared for the future.

Answered by GinnyAnswer | 2025-07-05

The total number of compounding periods is 36, and the interest rate per period is 1%.
;

Answered by Anonymous | 2025-07-20

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