(Related to Checkpoint 5.6) (Solving for ) You are considering investing in a security that will pay you $2,000 in 28 years. a. If the appropriate discount rate is 12 percent, what is the present value of this investment? b. Assume these investments sell for $853 in return for which you receive $2,000 in 28 years. What is the rate of return investors earn on this investment if they buy it for $853? a. If the appropriate discount rate is 12 percent, the present value of this investment is $. (Round to the nearest cent.) b. The rate of retum investors can earn on this investment if they buy it for $853 is%. (Round to two decimal places.)
(Related to Checkpoint 5.6) (Solving for ) You are considering investing in a security that will pay you $2,000 in 28 years. a. If the appropriate discount rate is 12 percent, what is the present value of this investment? b. Assume these investments sell for $853 in return for which you receive $2,000 in 28 years. What is the rate of return investors earn on this investment if they buy it for $853? a. If the appropriate discount rate is 12 percent, the present value of this investment is $. (Round to the nearest cent.) b. The rate of retum investors can earn on this investment if they buy it for $853 is%. (Round to two decimal places.)
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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![**Investment Valuation and Return Rate Calculation**
When considering an investment, it is essential to understand the present value of that investment and the potential rate of return. This exercise demonstrates these concepts using a practical example.
**Example Scenario:**
You are considering investing in a security that will pay you $2,000 in 28 years.
1. **Present Value Calculation:**
**Problem Statement:**
If the appropriate discount rate is 12 percent, what is the present value of this investment?
**Solution:**
To find the present value (PV) of the investment, use the present value formula:
\[
PV = \frac{FV}{(1 + r)^n}
\]
where:
- \( PV \) = Present Value
- \( FV \) = Future Value ($2,000)
- \( r \) = Discount rate (12% or 0.12)
- \( n \) = Number of years (28)
2. **Rate of Return Calculation:**
**Problem Statement:**
Assume these investments sell for $853 in return for which you receive $2,000 in 28 years. What is the rate of return investors can earn on this investment if they buy it for $853?
**Solution:**
To find the rate of return, use the future value formula rearranged to solve for \( r \):
\[
FV = PV \times (1 + r)^n
\]
\[
r = \left( \frac{FV}{PV} \right)^{\frac{1}{n}} - 1
\]
where:
- \( FV \) = Future Value ($2,000)
- \( PV \) = Present Value ($853)
- \( n \) = Number of years (28)
**Questions:**
a. If the appropriate discount rate is 12 percent, the present value of this investment is $ \_\_\_ (Round to the nearest cent.)
b. The rate of return investors can earn on this investment if they buy it for $853 is \_\_\_ % (Round to two decimal places.)
By understanding these calculations, you can make more informed decisions about potential investments and their value over time.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ff6323c-cf7e-493a-b269-a8fbd92b416a%2F3b9eb425-9c89-40a2-8850-43eacb6bb404%2Fjr8jlnb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Investment Valuation and Return Rate Calculation**
When considering an investment, it is essential to understand the present value of that investment and the potential rate of return. This exercise demonstrates these concepts using a practical example.
**Example Scenario:**
You are considering investing in a security that will pay you $2,000 in 28 years.
1. **Present Value Calculation:**
**Problem Statement:**
If the appropriate discount rate is 12 percent, what is the present value of this investment?
**Solution:**
To find the present value (PV) of the investment, use the present value formula:
\[
PV = \frac{FV}{(1 + r)^n}
\]
where:
- \( PV \) = Present Value
- \( FV \) = Future Value ($2,000)
- \( r \) = Discount rate (12% or 0.12)
- \( n \) = Number of years (28)
2. **Rate of Return Calculation:**
**Problem Statement:**
Assume these investments sell for $853 in return for which you receive $2,000 in 28 years. What is the rate of return investors can earn on this investment if they buy it for $853?
**Solution:**
To find the rate of return, use the future value formula rearranged to solve for \( r \):
\[
FV = PV \times (1 + r)^n
\]
\[
r = \left( \frac{FV}{PV} \right)^{\frac{1}{n}} - 1
\]
where:
- \( FV \) = Future Value ($2,000)
- \( PV \) = Present Value ($853)
- \( n \) = Number of years (28)
**Questions:**
a. If the appropriate discount rate is 12 percent, the present value of this investment is $ \_\_\_ (Round to the nearest cent.)
b. The rate of return investors can earn on this investment if they buy it for $853 is \_\_\_ % (Round to two decimal places.)
By understanding these calculations, you can make more informed decisions about potential investments and their value over time.
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