Use the savings plan formula to answer the following question. Your goal is to create a college fund for your child. Suppose you find a fund that offers an APR of 6%. How much should you deposit monthly to accumulate S$80,000 in 15 years? You should invest $ each month. (Do not round until the final answer. Then round to two decimal places as needed.)
Use the savings plan formula to answer the following question. Your goal is to create a college fund for your child. Suppose you find a fund that offers an APR of 6%. How much should you deposit monthly to accumulate S$80,000 in 15 years? You should invest $ each month. (Do not round until the final answer. Then round to two decimal places as needed.)
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
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Educational Saving Plan Example
**Question:**
Use the savings plan formula to answer the following question.
Your goal is to create a college fund for your child. Suppose you find a fund that offers an APR of 6%. How much should you deposit monthly to accumulate $80,000 in 15 years?
**Answer:**
You should invest $ ____ each month.
*(Do not round until the final answer. Then round to two decimal places as needed.)*
**Explanation:**
In this example, you are given the task of determining the monthly deposit needed to save $80,000 over 15 years with an annual percentage rate (APR) of 6%. The savings plan formula can be applied to calculate the necessary monthly deposit.
1. **Identify the variables:**
- Future value (FV): $80,000
- Annual interest rate (r): 6%
- Number of years (t): 15
- Monthly deposits (PMT): (What we need to find)
2. **Formula to use:**
The formula for the future value of an annuity (regular payments) is:
\[ FV = PMT \times \left[ \frac{(1 + \frac{r}{n})^{nt} - 1}{\frac{r}{n}} \right] \]
Where:
- \( FV \) is the future value.
- \( PMT \) is the monthly payment.
- \( r \) is the annual interest rate (as a decimal).
- \( n \) is the number of times compounding occurs per year (monthly compounding means \( n = 12 \)).
- \( t \) is the number of years.
3. **Calculation:**
Plug the values into the formula and solve for \( PMT \):
\[ 80000 = PMT \times \left[ \frac{(1 + \frac{0.06}{12})^{12 \times 15} - 1}{\frac{0.06}{12}} \right] \]
Solve the equation to find the value of \( PMT \).
4. **Final step:**
Once you've calculated the exact monthly deposit (do not round intermediate steps), round the final result to two decimal places to get the amount you need to invest each month.
Expanding the explanation and breaking down each step ensures clarity and comprehension for students visiting the educational website.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F89a4a128-932d-4e64-81ee-84f9e6b7c521%2F11c3408e-7b3c-4f1a-b49a-3417ca9901cc%2F1wc5rkr_processed.png&w=3840&q=75)
Transcribed Image Text:### Educational Saving Plan Example
**Question:**
Use the savings plan formula to answer the following question.
Your goal is to create a college fund for your child. Suppose you find a fund that offers an APR of 6%. How much should you deposit monthly to accumulate $80,000 in 15 years?
**Answer:**
You should invest $ ____ each month.
*(Do not round until the final answer. Then round to two decimal places as needed.)*
**Explanation:**
In this example, you are given the task of determining the monthly deposit needed to save $80,000 over 15 years with an annual percentage rate (APR) of 6%. The savings plan formula can be applied to calculate the necessary monthly deposit.
1. **Identify the variables:**
- Future value (FV): $80,000
- Annual interest rate (r): 6%
- Number of years (t): 15
- Monthly deposits (PMT): (What we need to find)
2. **Formula to use:**
The formula for the future value of an annuity (regular payments) is:
\[ FV = PMT \times \left[ \frac{(1 + \frac{r}{n})^{nt} - 1}{\frac{r}{n}} \right] \]
Where:
- \( FV \) is the future value.
- \( PMT \) is the monthly payment.
- \( r \) is the annual interest rate (as a decimal).
- \( n \) is the number of times compounding occurs per year (monthly compounding means \( n = 12 \)).
- \( t \) is the number of years.
3. **Calculation:**
Plug the values into the formula and solve for \( PMT \):
\[ 80000 = PMT \times \left[ \frac{(1 + \frac{0.06}{12})^{12 \times 15} - 1}{\frac{0.06}{12}} \right] \]
Solve the equation to find the value of \( PMT \).
4. **Final step:**
Once you've calculated the exact monthly deposit (do not round intermediate steps), round the final result to two decimal places to get the amount you need to invest each month.
Expanding the explanation and breaking down each step ensures clarity and comprehension for students visiting the educational website.
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