You would like to give your daughter $75,000 towards her college education 17 years from now. How much money must you set aside today for this purpose if you can earn 8 percent on your investments?
You would like to give your daughter $75,000 towards her college education 17 years from now. How much money must you set aside today for this purpose if you can earn 8 percent on your investments?
Algebra and Trigonometry (6th Edition)
6th Edition
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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Question
![**Future Value of College Savings**
**Question:**
You would like to give your daughter $75,000 towards her college education 17 years from now. How much money must you set aside today for this purpose if you can earn 8 percent on your investments?
---
**Answer:**
To determine how much money you need to set aside today to reach your goal of $75,000 in 17 years with an 8% annual return, you can use the present value formula of compound interest:
\[ PV = \frac{FV}{(1 + r)^n} \]
Where:
- \( PV \) = Present Value (the amount you need to invest today)
- \( FV \) = Future Value ($75,000)
- \( r \) = Annual interest rate (8% or 0.08)
- \( n \) = Number of years (17)
Plugging in the values:
\[ PV = \frac{75000}{(1 + 0.08)^{17}} \]
First, calculate \( (1 + 0.08)^{17} \):
\[ (1 + 0.08)^{17} = 3.938 \]
Now, divide the future value by this number to find the present value:
\[ PV = \frac{75000}{3.938} = 19051.59 \]
Therefore, you must set aside approximately $19,051.59 today to have $75,000 in 17 years, given an annual return of 8%.
---
**Question 6**
Below the primary question, you see the start of another problem (Question 6), but it is not visible in its entirety. Therefore, it is not included in this transcription.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fab2cae91-b738-4378-9d2b-34dbb8327a9e%2Fd8a6f735-3991-454c-91b9-d74618dcb1ad%2Fvq9nym8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Future Value of College Savings**
**Question:**
You would like to give your daughter $75,000 towards her college education 17 years from now. How much money must you set aside today for this purpose if you can earn 8 percent on your investments?
---
**Answer:**
To determine how much money you need to set aside today to reach your goal of $75,000 in 17 years with an 8% annual return, you can use the present value formula of compound interest:
\[ PV = \frac{FV}{(1 + r)^n} \]
Where:
- \( PV \) = Present Value (the amount you need to invest today)
- \( FV \) = Future Value ($75,000)
- \( r \) = Annual interest rate (8% or 0.08)
- \( n \) = Number of years (17)
Plugging in the values:
\[ PV = \frac{75000}{(1 + 0.08)^{17}} \]
First, calculate \( (1 + 0.08)^{17} \):
\[ (1 + 0.08)^{17} = 3.938 \]
Now, divide the future value by this number to find the present value:
\[ PV = \frac{75000}{3.938} = 19051.59 \]
Therefore, you must set aside approximately $19,051.59 today to have $75,000 in 17 years, given an annual return of 8%.
---
**Question 6**
Below the primary question, you see the start of another problem (Question 6), but it is not visible in its entirety. Therefore, it is not included in this transcription.
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