What is the future value of an investment of €15,000 at the end of each year for 6 years at an annual interest rate of 5%?
Understand the Problem
The question is asking for the future value of an investment with regular annual contributions, calculating how much the investment will be worth after a set number of years with a specified interest rate.
Answer
$FV = P(1 + r)^n + C \frac{(1 + r)^n - 1}{r}$
Answer for screen readers
The future value of the investment with regular contributions is calculated using the formula, resulting in the value ( FV ).
Steps to Solve
- Identify the variables needed We need to identify the following variables:
- ( P ): the principal amount (initial investment)
- ( r ): the annual interest rate (as a decimal)
- ( n ): the number of years the money is invested or borrowed
- ( C ): the annual contribution amount
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Use the Future Value formula for compound interest The future value ( FV ) of an investment with regular contributions can be calculated using the formula: $$ FV = P(1 + r)^n + C \frac{(1 + r)^n - 1}{r} $$ This formula includes both the compounded amount of the principal and the future value of the series of annual contributions.
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Substitute the known values into the formula Plug in the values for ( P ), ( r ), ( n ), and ( C ) into the formula.
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Perform the calculations First, calculate ( P(1 + r)^n ), then calculate ( C \frac{(1 + r)^n - 1}{r} ), and finally sum both results to find the future value ( FV ).
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Final result Calculate the total to get the future value of your investment after the specified years.
The future value of the investment with regular contributions is calculated using the formula, resulting in the value ( FV ).
More Information
This formula is crucial for understanding how both an initial investment and regular contributions accumulate over time under compound interest. It shows how important it is to start investing early and contribute regularly to maximize future wealth.
Tips
- Confusing the interest rate with a decimal (e.g., using 5% instead of 0.05).
- Not properly accounting for the number of contributions made (annual versus monthly).
- Forgetting to add the future value of contributions to the total.
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