Use the compound interest formulas to solve. 11) Find the accumulated value of an investment of \( \$ 1900 \) at \( 10 \% \) compounded quarterly for 5 years.
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Alright, let's crunch some numbers! The formula for compound interest is \( A = P \left(1 + \frac{r}{n}\right)^{nt} \), where \( A \) is the accumulated amount, \( P \) is the principal amount, \( r \) is the annual interest rate, \( n \) is the number of times interest is compounded per year, and \( t \) is the number of years. For your investment of \( P = 1900 \), \( r = 0.10 \), \( n = 4 \) (quarterly), and \( t = 5 \): Plugging in those numbers gives us: \[ A = 1900 \left(1 + \frac{0.10}{4}\right)^{4 \times 5} = 1900 \left(1 + 0.025\right)^{20} \] Calculating that, we find: \[ A = 1900 \left(1.025\right)^{20} \approx 1900 \times 1.280084 = 2432.16 \] So, the accumulated value of your investment after 5 years will be approximately \( \$2432.16 \). Happy investing!