You are considering a savings bond that will pay $100 in 8 years. If the interest rate is 1.9%, what should you pay today for the bond? The amount that you should pay today for the bond is $ (Round to the nearest cent.)
You are considering a savings bond that will pay $100 in 8 years. If the interest rate is 1.9%, what should you pay today for the bond? The amount that you should pay today for the bond is $ (Round to the nearest cent.)
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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Question
![**Savings Bond Valuation**
Let's consider a scenario where you are thinking about investing in a savings bond that will pay $100 in 8 years. To determine whether this investment is worth it, you need to calculate the present value of the bond using the given interest rate.
**Problem Statement:**
You are considering a savings bond that will pay $100 in 8 years. If the interest rate is 1.9%, what should you pay today for the bond?
**Calculation:**
To find the amount that you should pay today for the bond, calculate its present value using the formula for present value (PV):
\[ PV = \frac{FV}{(1 + r)^n} \]
Where:
- \( PV \) is the present value.
- \( FV \) is the future value of the bond ($100).
- \( r \) is the interest rate (1.9% or 0.019 as a decimal).
- \( n \) is the number of years until maturity (8 years).
Plugging in the values:
\[ PV = \frac{100}{(1 + 0.019)^8} \]
Solve for \( PV \) to determine the amount you should pay today for the bond.
**Result:**
The amount that you should pay today for the bond is $□□. (Round to the nearest cent.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F44f9ebf7-05a0-44a3-89d0-aa50ed2840a0%2Fe08c212b-2732-4a0a-bfce-fd3000e07fc9%2Fnrx8i1s.jpeg&w=3840&q=75)
Transcribed Image Text:**Savings Bond Valuation**
Let's consider a scenario where you are thinking about investing in a savings bond that will pay $100 in 8 years. To determine whether this investment is worth it, you need to calculate the present value of the bond using the given interest rate.
**Problem Statement:**
You are considering a savings bond that will pay $100 in 8 years. If the interest rate is 1.9%, what should you pay today for the bond?
**Calculation:**
To find the amount that you should pay today for the bond, calculate its present value using the formula for present value (PV):
\[ PV = \frac{FV}{(1 + r)^n} \]
Where:
- \( PV \) is the present value.
- \( FV \) is the future value of the bond ($100).
- \( r \) is the interest rate (1.9% or 0.019 as a decimal).
- \( n \) is the number of years until maturity (8 years).
Plugging in the values:
\[ PV = \frac{100}{(1 + 0.019)^8} \]
Solve for \( PV \) to determine the amount you should pay today for the bond.
**Result:**
The amount that you should pay today for the bond is $□□. (Round to the nearest cent.)
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