How much would $120 invested at 6% interest compounded monthly be worth after 21 years? Round your answer to the nearest cent.
[tex]A(t)=P\left(1+\frac{r}{n}\right)^{n t}[/tex]
A. $421.72
B. $271.20
C. $133.25
D. $407.95
Answer (1)
Substitute the given values into the compound interest formula.
Calculate the value inside the parentheses: 1 + 12 0.06 = 1.005 .
Calculate the exponent: 12 ⋅ 21 = 252 .
Calculate the future value and round to the nearest cent: $421.72 .
Explanation
Understanding the Problem We are given the principal amount P = $120 , the annual interest rate r = 6% = 0.06 , the number of times the interest is compounded per year n = 12 (monthly), and the number of years t = 21 . We want to find the future value A ( t ) of the investment after 21 years using the formula A ( t ) = P ( 1 + n r ) n t .
Substituting the Values Substitute the given values into the compound interest formula: A ( 21 ) = 120 ( 1 + 12 0.06 ) 12 ⋅ 21
Calculating the Parentheses Calculate the value inside the parentheses: 1 + 12 0.06 = 1 + 0.005 = 1.005
Calculating the Exponent Calculate the exponent: 12 ⋅ 21 = 252
Calculating the Future Value Calculate the future value: A ( 21 ) = 120 ( 1.005 ) 252 . We find that ( 1.005 ) 252 ≈ 3.51437064469923 .
Finding the Final Amount Multiply the result by 120 to get the final amount A ( 21 ) = 120 × 3.51437064469923 ≈ 421.7244773639076 .
Rounding the Answer Round the final amount to the nearest cent: A ( 21 ) ≈ $421.72 .
Examples
Compound interest is a powerful tool for growing wealth over time. For example, understanding compound interest can help you plan for retirement. If you invest $500 per month in a retirement account with an average annual return of 7% compounded monthly, you can calculate how much you'll have saved after 30 years. This knowledge allows you to make informed decisions about your savings and investment strategies to reach your financial goals.
