You bought a house for $75,000. You were told that it will increase in value by 2% a year. How much will it be worth after 12 years?
You bought a house for $75,000. You were told that it will increase in value by 2% a year. How much will it be worth after 12 years?
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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Question
![### Understanding Compound Interest
You bought a house for $75,000. You were told that it will increase in value by 2% a year. How much will it be worth after 12 years?
**Options:**
- a) $93,253.07
- b) $95,118.13
- c) $97,020.50
- d) $92,253.07
This problem is an example of compound interest calculation, where you determine the future value of an investment after a certain number of years, given an annual increase rate.
To solve this, you can use the formula for compound interest:
\[ A = P (1 + r)^n \]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (initial investment) - $75,000 in this case.
- \( r \) is the annual interest rate (decimal) - 0.02 in this case.
- \( n \) is the number of years the money is invested - 12 years in this case.
Plug in the numbers:
\[ A = 75000 \times (1 + 0.02)^{12} \]
Calculate to find the correct answer from the provided options.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff2a26d62-f5b2-42c9-9720-1adbdcac00ca%2Fdc286788-fdf2-48b8-b24e-006c82c2211c%2F7h5mvm8_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding Compound Interest
You bought a house for $75,000. You were told that it will increase in value by 2% a year. How much will it be worth after 12 years?
**Options:**
- a) $93,253.07
- b) $95,118.13
- c) $97,020.50
- d) $92,253.07
This problem is an example of compound interest calculation, where you determine the future value of an investment after a certain number of years, given an annual increase rate.
To solve this, you can use the formula for compound interest:
\[ A = P (1 + r)^n \]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (initial investment) - $75,000 in this case.
- \( r \) is the annual interest rate (decimal) - 0.02 in this case.
- \( n \) is the number of years the money is invested - 12 years in this case.
Plug in the numbers:
\[ A = 75000 \times (1 + 0.02)^{12} \]
Calculate to find the correct answer from the provided options.
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