The present worth of a deposit of $1,000 now and $1,000 every six months for 10 years at an interest rate of 10% per year, compounded semiannually is represented by which of the following equations Multiple Choice P=1,000(P/A, 5%, 21) (F/P, 5%, 1). P-1,000 (P/A, 5%, 20). P=1,000 (P/A, 5%, 21). P-1,000+ 1,000(P/A, 10.25%, 10).
The present worth of a deposit of $1,000 now and $1,000 every six months for 10 years at an interest rate of 10% per year, compounded semiannually is represented by which of the following equations Multiple Choice P=1,000(P/A, 5%, 21) (F/P, 5%, 1). P-1,000 (P/A, 5%, 20). P=1,000 (P/A, 5%, 21). P-1,000+ 1,000(P/A, 10.25%, 10).
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:**Problem Statement:**
The present worth of a deposit of $1,000 now and $1,000 every six months for 10 years at an interest rate of 10% per year, compounded semiannually, is represented by which of the following equations?
**Multiple Choice Options:**
1. \( P = 1,000(P/A, 5\%, 21) + (P/F, 5\%, 1) \)
2. \( P = 1,000(P/A, 5\%, 20) \)
3. \( P = 1,000(P/A, 5\%, 21) \)
4. \( P = 1,000 + 1,000(P/A, 10.25\%, 10) \)
**Solution:**
- The correct choice is highlighted in the image.
**Explanation of Symbols:**
- \( P \) refers to the present worth.
- \( (P/A, i\%, n) \) refers to the present value factor for an annuity, where \( i \% \) is the interest rate per period and \( n \) is the number of periods.
- \( (P/F, i\%, n) \) refers to the present value factor for a single sum, where \( i \% \) is the interest rate per period and \( n \) is the number of periods.
**Selection Explanation:**
- To calculate the present worth of an annuity compounded semiannually at an annual interest rate of 10%, the effective interest rate per period is 5% (half of the annual rate), and the number of periods is 20 (since there are 2 periods per year for 10 years).
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