Steven Combs is the grand prize winner in a college tuition essay contest. He will receive $7,000 at the beginning of each year for the next 5 years. How much (in $) should be invested at 8% interest compounded annually to award the prize?
Steven Combs is the grand prize winner in a college tuition essay contest. He will receive $7,000 at the beginning of each year for the next 5 years. How much (in $) should be invested at 8% interest compounded annually to award the prize?
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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Use Table 12-2
*I am having trouble understanding how to get the answer. I always come up with something different. I am must round to the nearest cent*
Steven Combs is the grand prize winner in a college tuition essay contest.
He will receive $7,000 at the beginning of each year for the next 5 years.
How much (in $) should be invested at 8% interest compounded annually to award the prize?
![**Table 12.2 - Present Value (Amount) of an Ordinary Annuity of $1**
This table provides the present value factors for an ordinary annuity of $1, across various interest rates and periods. The values allow for the calculation of the present value of an annuity that pays $1 at the end of each period.
**Columns and Rows:**
- **Periods:** Listed from 1 to 40. This indicates the total number of periods in the annuity.
- **Interest Rates:** Ranging from 0.5% to 18%, across several columns. This reflects the interest rate per period.
For each combination of interest rate and number of periods, the table provides a factor that, when multiplied by the payment amount ($1), yields the present value of the annuity.
**Formula:**
The values in Table 12.2 were generated using the formula:
\[ PV = \frac{{1 - (1 + i)^{-n}}}{i} \]
where:
- \( i \) is the interest rate per period,
- \( n \) is the total number of periods.
The values are rounded to five decimal places.
### Explanation of Use:
To determine the present value of an ordinary annuity:
1. Locate the appropriate interest rate column.
2. Find the row that corresponds to the number of periods.
3. Multiply the factor by the annuity payment amount to obtain the present value.
This table is useful for financial professionals in calculating loans, mortgages, or any scenario where an annuity structure is used. It helps in understanding the time value of money by determining how much a series of future payments is worth today.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F128a1981-67b4-46d9-9fae-0a17917a39e7%2F3131d94a-dfa0-4a41-8035-ac3aad93981b%2Fkxeh7mu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Table 12.2 - Present Value (Amount) of an Ordinary Annuity of $1**
This table provides the present value factors for an ordinary annuity of $1, across various interest rates and periods. The values allow for the calculation of the present value of an annuity that pays $1 at the end of each period.
**Columns and Rows:**
- **Periods:** Listed from 1 to 40. This indicates the total number of periods in the annuity.
- **Interest Rates:** Ranging from 0.5% to 18%, across several columns. This reflects the interest rate per period.
For each combination of interest rate and number of periods, the table provides a factor that, when multiplied by the payment amount ($1), yields the present value of the annuity.
**Formula:**
The values in Table 12.2 were generated using the formula:
\[ PV = \frac{{1 - (1 + i)^{-n}}}{i} \]
where:
- \( i \) is the interest rate per period,
- \( n \) is the total number of periods.
The values are rounded to five decimal places.
### Explanation of Use:
To determine the present value of an ordinary annuity:
1. Locate the appropriate interest rate column.
2. Find the row that corresponds to the number of periods.
3. Multiply the factor by the annuity payment amount to obtain the present value.
This table is useful for financial professionals in calculating loans, mortgages, or any scenario where an annuity structure is used. It helps in understanding the time value of money by determining how much a series of future payments is worth today.
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