Suppose that you earned a bachelor's degree and now you're teaching high school. The school district offers teachers the opportunity to take a year off to earn a master's degree. To achieve this goal, you deposit $3000 at the end of each year in an annuity that pays 6% compounded annually. a. b. How much will you have saved at the end of five years? Find the interest. Click the icon to view some finance formulas. a. After 5 years, you will have approximately $ (Do not round until the final answer. Then round to the nearest dollar as needed.) b. The interest is approximately $ (Use the answer from part a to find this answer.)
Suppose that you earned a bachelor's degree and now you're teaching high school. The school district offers teachers the opportunity to take a year off to earn a master's degree. To achieve this goal, you deposit $3000 at the end of each year in an annuity that pays 6% compounded annually. a. b. How much will you have saved at the end of five years? Find the interest. Click the icon to view some finance formulas. a. After 5 years, you will have approximately $ (Do not round until the final answer. Then round to the nearest dollar as needed.) b. The interest is approximately $ (Use the answer from part a to find this answer.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:**Educational Content: Annuity Savings Calculation**
**Scenario:**
Suppose you have earned a bachelor's degree and are now teaching high school. The school district offers teachers the opportunity to take a year off to earn a master's degree. To achieve this goal, you deposit $3000 at the end of each year in an annuity that pays 6% compounded annually.
**Tasks:**
**a.** How much will you have saved at the end of five years?
**b.** Find the interest.
_Click the icon to view some finance formulas._
**Calculations:**
**a.** After 5 years, you will have approximately $____.
(Do not round until the final answer. Then round to the nearest dollar as needed.)
**b.** The interest is approximately $____.
(Use the answer from part a to find this answer.)
![In the following formulas, \( P \) is the deposit made at the end of each compounding period, \( r \) is the annual interest rate of the annuity in decimal form, \( n \) is the number of compounding periods per year, and \( A \) is the value of the annuity after \( t \) years.
The formula for the future value of an annuity is:
\[
A = \frac{P \left( (1 + r)^t - 1 \right)}{r}
\]
An alternative expression using compounding variables is:
\[
A = P \left[ \frac{\left( 1 + \frac{r}{n} \right)^{nt} - 1}{\frac{r}{n}} \right]
\]
To find the deposit amount \( P \) when \( A \) is known, the formula is:
\[
P = \frac{A \left( \frac{r}{n} \right)}{\left( 1 + \frac{r}{n} \right)^{nt} - 1}
\]
In the subsequent formulas, \( P \) is the principal amount deposited into an account, \( r \) is the annual interest rate in decimal form, \( n \) is the number of compounding periods per year, and \( A \) is the future value of the account after \( t \) years.
The formula for future value with simple interest:
\[
A = P(1 + rt)
\]
The formula for future value with compound interest:
\[
A = P \left( 1 + \frac{r}{n} \right)^{nt}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd8776e5e-a1de-48d6-ac3e-f9f0f44d4219%2Fa207294e-4cb6-4915-b38d-b93ebd439f08%2Ff5oj6qi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In the following formulas, \( P \) is the deposit made at the end of each compounding period, \( r \) is the annual interest rate of the annuity in decimal form, \( n \) is the number of compounding periods per year, and \( A \) is the value of the annuity after \( t \) years.
The formula for the future value of an annuity is:
\[
A = \frac{P \left( (1 + r)^t - 1 \right)}{r}
\]
An alternative expression using compounding variables is:
\[
A = P \left[ \frac{\left( 1 + \frac{r}{n} \right)^{nt} - 1}{\frac{r}{n}} \right]
\]
To find the deposit amount \( P \) when \( A \) is known, the formula is:
\[
P = \frac{A \left( \frac{r}{n} \right)}{\left( 1 + \frac{r}{n} \right)^{nt} - 1}
\]
In the subsequent formulas, \( P \) is the principal amount deposited into an account, \( r \) is the annual interest rate in decimal form, \( n \) is the number of compounding periods per year, and \( A \) is the future value of the account after \( t \) years.
The formula for future value with simple interest:
\[
A = P(1 + rt)
\]
The formula for future value with compound interest:
\[
A = P \left( 1 + \frac{r}{n} \right)^{nt}
\]
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