If $240 is invested at an interest rate of $9 \% per year and is compounded monthly, how much will the investment be worth in 14 years?
Use the compound interest formula [tex]A=P\left(1+\frac{r}{n}\right)^{n t}[/tex].
Answer (1)
Substitute the given values into the compound interest formula: A = 240 ( 1 + 12 0.09 ) ( 12 ) ( 14 ) .
Simplify the expression inside the parentheses: 1 + 12 0.09 = 1.0075 .
Calculate the exponent: ( 12 ) ( 14 ) = 168 .
Calculate the future value: A = 240 × ( 1.0075 ) 168 ≈ $842.13 .
Explanation
Understanding the Problem We are given the principal amount P = $240 , the annual interest rate r = 9% = 0.09 , the number of times the interest is compounded per year n = 12 (monthly), and the number of years t = 14 . We want to find the future value A of the investment using the compound interest formula: A = P ( 1 + n r ) n t
Substituting the Values Substitute the given values into the formula: A = 240 ( 1 + 12 0.09 ) ( 12 ) ( 14 )
Simplifying the Fraction First, we simplify the expression inside the parentheses: 12 0.09 = 0.0075 So, 1 + 12 0.09 = 1 + 0.0075 = 1.0075
Calculating the Exponent Next, we calculate the exponent: ( 12 ) ( 14 ) = 168
Calculating the Power Now, we calculate the value of ( 1.0075 ) 168 : ( 1.0075 ) 168 ≈ 3.508885595
Calculating the Future Value Finally, we multiply the result by the principal amount: A = 240 × 3.508885595 ≈ 842.132543 Rounding to two decimal places, we get A ≈ $842.13 .
Final Answer Therefore, the investment will be worth approximately $842.13 in 14 years.
Examples
Compound interest is a powerful tool for growing wealth over time. For example, if you invest $1 , 000 in a retirement account with an average annual return of 7% compounded monthly, after 30 years, your investment could grow significantly. Understanding compound interest helps you make informed decisions about savings, investments, and loans, allowing you to plan for your financial future effectively. It's a fundamental concept in personal finance and economics.
