$15,000 at 15% compounded annually for 5 years
A. $28,500.00
0
B. $30,170.36
C. $17.250.00
ОО
D. $26,250.45
The Correct Answer and Explanation is :
To calculate the future value of an investment using compound interest, we can use the formula:
[
A = P(1 + r)^n
]
Where:
- ( A ) is the future value of the investment/loan, including interest
- ( P ) is the principal investment amount (the initial deposit or loan amount)
- ( r ) is the annual interest rate (decimal)
- ( n ) is the number of years the money is invested or borrowed
Given:
- ( P = 15,000 )
- ( r = 0.15 ) (15% expressed as a decimal)
- ( n = 5 )
Plugging in the values:
[
A = 15000(1 + 0.15)^5
]
Calculating step-by-step:
- Calculate ( 1 + r ):
[
1 + 0.15 = 1.15
] - Raise ( 1.15 ) to the power of ( 5 ):
[
1.15^5 \approx 2.011357
] - Multiply this result by the principal ( P ):
[
A \approx 15000 \times 2.011357 \approx 30170.36
]
Therefore, the future value ( A ) is approximately $30,170.36.
Explanation
The calculation demonstrates the power of compound interest, where interest is earned not only on the initial principal but also on the accumulated interest from previous periods. In this example, starting with a principal of $15,000 and compounding annually at a rate of 15%, the investment grows significantly over five years.
Each year, the interest earned is added to the principal, resulting in a larger base for the calculation of interest in the following year. This leads to exponential growth, which can be contrasted with simple interest, where only the principal earns interest.
The final amount of $30,170.36 represents a substantial return on the original investment, showcasing the importance of understanding and utilizing compound interest in personal finance and investment strategies. It highlights how strategic investment decisions can lead to financial growth over time, making it a valuable concept for both individual and institutional investors. Thus, the correct answer is B. $30,170.36.