Suppose that you want to avoid paying interest and decide you'll only buy the furniture when you have the money to pay for it. An annuity is basically the opposite of a fixed-installment loan: you deposit a fixed amount each month and receive interest based on the total amount that's been saved. The future value formula is: A = r 12M [(1 + 2)²-1] r r t where M is the regular monthly payment, is the annual interest rate in decimal form, and is the term of the annuity in years. With a monthly payment of $110, what would the future value be if you chose an annuity with a term of two years at 4.7% interest? Round you answer to the nearest cent.
Suppose that you want to avoid paying interest and decide you'll only buy the furniture when you have the money to pay for it. An annuity is basically the opposite of a fixed-installment loan: you deposit a fixed amount each month and receive interest based on the total amount that's been saved. The future value formula is: A = r 12M [(1 + 2)²-1] r r t where M is the regular monthly payment, is the annual interest rate in decimal form, and is the term of the annuity in years. With a monthly payment of $110, what would the future value be if you chose an annuity with a term of two years at 4.7% interest? Round you answer 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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![# Understanding Future Value of Annuities
Suppose that you want to avoid paying interest and decide you'll only buy the furniture when you have the money to pay for it. An annuity is basically the opposite of a fixed-installment loan: you deposit a fixed amount each month and receive interest based on the total amount that's been saved.
The future value formula for an annuity is:
\[ A = \frac{12M \left( \left(1 + \frac{r}{12}\right)^{12t} - 1 \right)}{r} \]
where:
- \( M \) is the regular monthly payment.
- \( r \) is the annual interest rate in decimal form.
- \( t \) is the term of the annuity in years.
### Example Calculation:
With a monthly payment of \(\$110\), what would the future value be if you chose an annuity with a term of two years at \(4.7\%\) interest? Round your answer to the nearest cent.
First, convert the annual interest rate to a decimal:
\[ r = \frac{4.7}{100} = 0.047 \]
Substitute the values into the future value formula:
\[ M = 110 \]
\[ t = 2 \]
\[ r = 0.047 \]
Plug these values into the formula and compute the future value:
\[ A = \frac{12 \times 110 \left( \left(1 + \frac{0.047}{12}\right)^{12 \times 2} - 1 \right)}{0.047} \]
This will give you the future value of the annuity after 2 years of monthly payments of \(\$110\) at an annual interest rate of \(4.7\%\).
Calculate the numerical result to determine the answer which will be rounded to the nearest cent.
### Supporting Diagram Explanation:
There are no diagrams or graphs provided in the given image.
This explanation illustrates how the future value of an annuity can be calculated and provides a clear, step-by-step guide to applying the formula to a practical example. This is particularly useful for understanding the impact of regular savings in an interest-earning account over a specified period.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf54cc92-fe70-42ec-a5a5-6c03b8447a69%2F0786fd9f-a27d-4278-8722-09e9e1ec004e%2F0ccxf6c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:# Understanding Future Value of Annuities
Suppose that you want to avoid paying interest and decide you'll only buy the furniture when you have the money to pay for it. An annuity is basically the opposite of a fixed-installment loan: you deposit a fixed amount each month and receive interest based on the total amount that's been saved.
The future value formula for an annuity is:
\[ A = \frac{12M \left( \left(1 + \frac{r}{12}\right)^{12t} - 1 \right)}{r} \]
where:
- \( M \) is the regular monthly payment.
- \( r \) is the annual interest rate in decimal form.
- \( t \) is the term of the annuity in years.
### Example Calculation:
With a monthly payment of \(\$110\), what would the future value be if you chose an annuity with a term of two years at \(4.7\%\) interest? Round your answer to the nearest cent.
First, convert the annual interest rate to a decimal:
\[ r = \frac{4.7}{100} = 0.047 \]
Substitute the values into the future value formula:
\[ M = 110 \]
\[ t = 2 \]
\[ r = 0.047 \]
Plug these values into the formula and compute the future value:
\[ A = \frac{12 \times 110 \left( \left(1 + \frac{0.047}{12}\right)^{12 \times 2} - 1 \right)}{0.047} \]
This will give you the future value of the annuity after 2 years of monthly payments of \(\$110\) at an annual interest rate of \(4.7\%\).
Calculate the numerical result to determine the answer which will be rounded to the nearest cent.
### Supporting Diagram Explanation:
There are no diagrams or graphs provided in the given image.
This explanation illustrates how the future value of an annuity can be calculated and provides a clear, step-by-step guide to applying the formula to a practical example. This is particularly useful for understanding the impact of regular savings in an interest-earning account over a specified period.
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