Jose invested $50,000 at 12% for 4 years compounded annually. What is the maturity value at the end of Year 3?
A. $56,000
B. $78,675.97
C. $62,720
D. $70,246.40
Answer (2)
We use the compound interest formula: A = P ( 1 + r ) n .
Substitute the given values: P = 50000 , r = 0.12 , and n = 3 .
Calculate A = 50000 ( 1 + 0.12 ) 3 = 50000 ( 1.12 ) 3 = 70246.40 .
The maturity value at the end of Year 3 is 70246.40 .
Explanation
Understanding the Problem We are given that Jose invested $50,000 at an annual interest rate of 12%, compounded annually, for a period of 4 years. We want to find the maturity value of the investment at the end of Year 3.
Applying the Compound Interest Formula To find the maturity value at the end of Year 3, we use the formula for compound interest: A = P ( 1 + r ) n where:
A is the maturity value
P is the principal amount ($50,000)
r is the annual interest rate (12% or 0.12)
n is the number of years (3)
Substituting the Values Substitute the given values into the formula: A = 50000 ( 1 + 0.12 ) 3
Calculating the Maturity Value Calculate the value: A = 50000 ( 1.12 ) 3 A = 50000 ( 1.404928 ) A = 70246.40
Final Answer Therefore, the maturity value at the end of Year 3 is $70,246.40.
Examples
Understanding compound interest is crucial for making informed financial decisions. For example, if you invest $10,000 in a mutual fund that yields an average annual return of 8%, compounded annually, you can calculate the future value of your investment after a certain number of years. This helps you estimate how much your investment will grow over time, enabling you to plan for long-term financial goals such as retirement or your children's education. By understanding the power of compounding, you can make strategic investment choices to maximize your returns.
The maturity value of Jose's investment at the end of Year 3 is approximately $70,246.40. This is calculated using the compound interest formula. The correct choice is option D: $70,246.40.
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