A merchant wants to have P2,000 to a small business for a period of 6 years. With a given interest rate on the investment of 15% compounded quarterly, how much will be the amount to invest?
A merchant wants to have P2,000 to a small business for a period of 6 years. With a given interest rate on the investment of 15% compounded quarterly, how much will be the amount to invest?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Note- Here P2000 is final amount
![**Compound Interest Calculation Example**
A merchant wants to invest in a small business and requires P2,000 for a period of 6 years. The investment offers an interest rate of 15% compounded quarterly. The question is: how much should be invested initially to reach the desired amount?
*Note: This is a compound interest problem.*
The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (initial investment).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of times that interest is compounded per year.
- \( t \) is the time in years.
Given:
- \( A = 2000 \)
- \( r = 0.15 \)
- \( n = 4 \) (since the interest is compounded quarterly)
- \( t = 6 \)
We need to solve for \( P \), the initial amount to invest.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F539d2b63-355c-4c6a-8aa3-291efa2717e0%2F37ce4937-57a1-47b5-b1c1-15e8ffa611f7%2Fvrsyq7q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Compound Interest Calculation Example**
A merchant wants to invest in a small business and requires P2,000 for a period of 6 years. The investment offers an interest rate of 15% compounded quarterly. The question is: how much should be invested initially to reach the desired amount?
*Note: This is a compound interest problem.*
The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (initial investment).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of times that interest is compounded per year.
- \( t \) is the time in years.
Given:
- \( A = 2000 \)
- \( r = 0.15 \)
- \( n = 4 \) (since the interest is compounded quarterly)
- \( t = 6 \)
We need to solve for \( P \), the initial amount to invest.
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