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= 12M 1+ r 12 r 12t -1 where M is the regular monthly payment, r is the annual interest rate in decimal form, and t is the term of the annuity in years. With a monthly payment of $120, what would the future value be if you chose an annuity with a term of two years at 4.8% interest? Round you answer to the nearest cent. The future value would be $ X
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= 12M 1+ r 12 r 12t -1 where M is the regular monthly payment, r is the annual interest rate in decimal form, and t is the term of the annuity in years. With a monthly payment of $120, what would the future value be if you chose an annuity with a term of two years at 4.8% interest? Round you answer to the nearest cent. The future value would be $ X
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![### Annuity Future Value Formula
When you want to avoid paying interest on a purchase, you can decide to save the money and only buy the item when you have the total amount. An annuity is a method that helps you achieve this by allowing you to deposit a fixed amount each month, which accumulates interest based on the total saved. Here's a detailed explanation of how you can calculate the future value of such an annuity.
**Future Value Formula:**
\[
A = \frac{12M \left[ \left(1 + \frac{r}{12}\right)^{12t} - 1 \right]}{r}
\]
Where:
- \(A\) is the future value of the annuity.
- \(M\) is the regular monthly payment.
- \(r\) is the annual interest rate in decimal form.
- \(t\) is the term of the annuity in years.
#### Example:
Suppose you plan to make a monthly payment of $120 and you choose an annuity with a term of 2 years at an annual interest rate of 4.8%. How would you calculate the future value?
1. **Monthly Payment (\(M\))**: $120
2. **Annual Interest Rate (\(r\))**: 4.8% or 0.048 in decimal form
3. **Term (\(t\))**: 2 years
Using these values in our formula:
\[
A = \frac{12 \times 120 \left[ \left(1 + \frac{0.048}{12}\right)^{12 \times 2} - 1 \right]}{0.048}
\]
#### Detailed Steps:
1. Convert the annual interest rate to a monthly rate by dividing by 12:
\[
\frac{0.048}{12} = 0.004
\]
2. Calculate \(1\) plus the monthly interest rate:
\[
1 + 0.004 = 1.004
\]
3. Raise this sum to the power of the total number of payments (12 payments per year times 2 years):
\[
1.004^{24}
\]
4. Subtract 1 from the result of the exponentiation:
\[
1.004^{24} - 1
\]
5](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf54cc92-fe70-42ec-a5a5-6c03b8447a69%2Fed2bc091-afd5-4d34-bd65-570f6a0f9d20%2F8uspyqk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Annuity Future Value Formula
When you want to avoid paying interest on a purchase, you can decide to save the money and only buy the item when you have the total amount. An annuity is a method that helps you achieve this by allowing you to deposit a fixed amount each month, which accumulates interest based on the total saved. Here's a detailed explanation of how you can calculate the future value of such an annuity.
**Future Value Formula:**
\[
A = \frac{12M \left[ \left(1 + \frac{r}{12}\right)^{12t} - 1 \right]}{r}
\]
Where:
- \(A\) is the future value of the annuity.
- \(M\) is the regular monthly payment.
- \(r\) is the annual interest rate in decimal form.
- \(t\) is the term of the annuity in years.
#### Example:
Suppose you plan to make a monthly payment of $120 and you choose an annuity with a term of 2 years at an annual interest rate of 4.8%. How would you calculate the future value?
1. **Monthly Payment (\(M\))**: $120
2. **Annual Interest Rate (\(r\))**: 4.8% or 0.048 in decimal form
3. **Term (\(t\))**: 2 years
Using these values in our formula:
\[
A = \frac{12 \times 120 \left[ \left(1 + \frac{0.048}{12}\right)^{12 \times 2} - 1 \right]}{0.048}
\]
#### Detailed Steps:
1. Convert the annual interest rate to a monthly rate by dividing by 12:
\[
\frac{0.048}{12} = 0.004
\]
2. Calculate \(1\) plus the monthly interest rate:
\[
1 + 0.004 = 1.004
\]
3. Raise this sum to the power of the total number of payments (12 payments per year times 2 years):
\[
1.004^{24}
\]
4. Subtract 1 from the result of the exponentiation:
\[
1.004^{24} - 1
\]
5
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 1 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman