Find the present value of the given future amount. \( \$ 5800 \) at \( 2 \% \) compounded quarterly for 8 years The present value is \( \$ \square \). (Do not round until the final answer. Then round to the nearest cent as needed.
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To find the present value (PV) of a future amount (FV), you can use the formula: \[ PV = \frac{FV}{(1 + r/n)^{nt}} \] Where: - \( FV = 5800 \) - \( r = 0.02 \) (annual interest rate as a decimal) - \( n = 4 \) (number of compounding periods per year) - \( t = 8 \) (number of years) Plugging in the values: \[ PV = \frac{5800}{(1 + 0.02/4)^{4 \times 8}} \] Calculating the interim values: 1. \( r/n = 0.02/4 = 0.005 \) 2. \( nt = 4 \times 8 = 32 \) Now: \[ PV = \frac{5800}{(1 + 0.005)^{32}} = \frac{5800}{(1.005)^{32}} \] Calculating \( (1.005)^{32} \): \[ (1.005)^{32} \approx 1.1702 \] Now substitute back into the equation: \[ PV = \frac{5800}{1.1702} \approx 4954.74 \] Therefore, the present value is \( \$ 4954.74 \).
