5. Betty will need $12,000 in five years to pay for a major overhaul on her tractor engine. She has found an investment that will provide a 10% return on her invested funds. How much does Betty need to invest today so she will have her overhaul funds in five years?
5. Betty will need $12,000 in five years to pay for a major overhaul on her tractor engine. She has found an investment that will provide a 10% return on her invested funds. How much does Betty need to invest today so she will have her overhaul funds in five years?
Chapter1: Making Economics Decisions
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![**Question 5: Future Investment Calculation**
Betty will need $12,000 in five years to pay for a major overhaul on her tractor engine. She has found an investment that will provide a 10% return on her invested funds. How much does Betty need to invest today so she will have her overhaul funds in five years?
**Explanation:**
To determine how much Betty needs to invest today, we use the concept of Present Value (PV) in finance. The Present Value formula for a future amount is given by:
\[ PV = \frac{FV}{(1 + r)^n} \]
Where:
- \( PV \) is the Present Value (the amount to invest today)
- \( FV \) is the Future Value (the amount needed in the future)
- \( r \) is the annual interest rate (expressed as a decimal)
- \( n \) is the number of years until the amount is needed
Given:
- \( FV = $12,000 \)
- \( r = 0.10 \) (10%)
- \( n = 5 \) years
Plugging these values into the formula:
\[ PV = \frac{12000}{(1 + 0.10)^5} \]
\[ PV = \frac{12000}{(1.10)^5} \]
\[ PV = \frac{12000}{1.61051} \]
\[ PV \approx 7,452.47 \]
So, Betty needs to invest approximately $7,452.47 today to have $12,000 in five years at a 10% annual return.
This principle can be applied to various investment scenarios to determine how much to invest currently to reach a specific future financial goal.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fce5cea56-9cd3-471d-b739-11e3ad279d5e%2F9b998132-6faa-44a0-a6ff-d060ad6caa8f%2Fxdjxg5o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 5: Future Investment Calculation**
Betty will need $12,000 in five years to pay for a major overhaul on her tractor engine. She has found an investment that will provide a 10% return on her invested funds. How much does Betty need to invest today so she will have her overhaul funds in five years?
**Explanation:**
To determine how much Betty needs to invest today, we use the concept of Present Value (PV) in finance. The Present Value formula for a future amount is given by:
\[ PV = \frac{FV}{(1 + r)^n} \]
Where:
- \( PV \) is the Present Value (the amount to invest today)
- \( FV \) is the Future Value (the amount needed in the future)
- \( r \) is the annual interest rate (expressed as a decimal)
- \( n \) is the number of years until the amount is needed
Given:
- \( FV = $12,000 \)
- \( r = 0.10 \) (10%)
- \( n = 5 \) years
Plugging these values into the formula:
\[ PV = \frac{12000}{(1 + 0.10)^5} \]
\[ PV = \frac{12000}{(1.10)^5} \]
\[ PV = \frac{12000}{1.61051} \]
\[ PV \approx 7,452.47 \]
So, Betty needs to invest approximately $7,452.47 today to have $12,000 in five years at a 10% annual return.
This principle can be applied to various investment scenarios to determine how much to invest currently to reach a specific future financial goal.
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