The compounding periods and the payment periods are the same for an annuity and for an amortization. Determine the present value of the annuity that will pay the given periodic payments. (Round your final answer to two decimal places.) Monthly payments of $460.80 for 4 years at 4.9% interest.
The compounding periods and the payment periods are the same for an annuity and for an amortization. Determine the present value of the annuity that will pay the given periodic payments. (Round your final answer to two decimal places.) Monthly payments of $460.80 for 4 years at 4.9% interest.
Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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The compounding periods and the payment periods are the same for an annuity and for an amortization. Determine the present value of the annuity that will pay the given periodic payments. (Round your final answer to two decimal places.)
Monthly payments of $460.80 for 4 years at 4.9% interest.
![### Calculating the Present Value of an Annuity
When the compounding periods and the payment periods are the same for an annuity and for an amortization, you can determine the present value of the annuity that will pay the given periodic payments.
**Problem Statement:**
Determine the present value of the annuity that will pay the given periodic payments. (Remember to round your final answer to two decimal places.)
**Given Data:**
- **Monthly payments:** $460.80
- **Duration:** 4 years
- **Interest rate:** 4.9%
### Explanation:
To find the present value of an annuity, you can use the present value formula for an ordinary annuity:
\[ PV = P \times \left( \dfrac{(1 - (1 + r)^{-n})}{r} \right) \]
Where:
- \( PV \) = Present Value of the annuity
- \( P \) = Payment amount per period ($460.80 in this case)
- \( r \) = Periodic interest rate (monthly in this case)
- \( n \) = Total number of payments (number of years multiplied by the number of periods per year)
Once you have all the values, plug them into the formula to calculate the present value of the annuity.
### Calculation:
To convert the annual interest rate to a monthly rate, you divide by 12:
\[ r = \dfrac{4.9\%}{12} = 0.0040833 \]
The total number of payments over 4 years, making monthly payments, will be:
\[ n = 4 \times 12 = 48 \]
Replace the variables in the formula:
\[ PV = 460.80 \times \left( \dfrac{(1 - (1 + 0.0040833)^{-48})}{0.0040833} \right) \]
Simplify the equation step-by-step to find the present value.
You can use a calculator or software to find the precise result.
Finally, enter your answer in the provided input box for final confirmation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff726d6fd-4af8-4bb0-826c-a6698fefcdb5%2Ff939d75b-0aa9-4426-ace3-2e2f9fe32577%2Fopbco3t_processed.png&w=3840&q=75)
Transcribed Image Text:### Calculating the Present Value of an Annuity
When the compounding periods and the payment periods are the same for an annuity and for an amortization, you can determine the present value of the annuity that will pay the given periodic payments.
**Problem Statement:**
Determine the present value of the annuity that will pay the given periodic payments. (Remember to round your final answer to two decimal places.)
**Given Data:**
- **Monthly payments:** $460.80
- **Duration:** 4 years
- **Interest rate:** 4.9%
### Explanation:
To find the present value of an annuity, you can use the present value formula for an ordinary annuity:
\[ PV = P \times \left( \dfrac{(1 - (1 + r)^{-n})}{r} \right) \]
Where:
- \( PV \) = Present Value of the annuity
- \( P \) = Payment amount per period ($460.80 in this case)
- \( r \) = Periodic interest rate (monthly in this case)
- \( n \) = Total number of payments (number of years multiplied by the number of periods per year)
Once you have all the values, plug them into the formula to calculate the present value of the annuity.
### Calculation:
To convert the annual interest rate to a monthly rate, you divide by 12:
\[ r = \dfrac{4.9\%}{12} = 0.0040833 \]
The total number of payments over 4 years, making monthly payments, will be:
\[ n = 4 \times 12 = 48 \]
Replace the variables in the formula:
\[ PV = 460.80 \times \left( \dfrac{(1 - (1 + 0.0040833)^{-48})}{0.0040833} \right) \]
Simplify the equation step-by-step to find the present value.
You can use a calculator or software to find the precise result.
Finally, enter your answer in the provided input box for final confirmation.
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