suppose a state of california bond will pay $1,000 eight years from now. if the going interest rate on these…

Explanation:

Step1: Present the present - value formula

The present - value formula for a single future cash flow is (PV=\frac{FV}{(1 + r)^{n}}), where (PV) is the present value, (FV) is the future value, (r) is the interest rate, and (n) is the number of periods. Here, (FV = 1000), (r=0.066), and (n = 8).

Step2: Substitute the values into the formula

[ \begin{align*} PV&=\frac{1000}{(1 + 0.066)^{8}}\ &=\frac{1000}{1.066^{8}} \end{align*} ]

Step3: Calculate (1.066^{8})

Using a calculator, (1.066^{8}\approx1.698)

Step4: Calculate the present value

[ PV=\frac{1000}{1.698}\approx588.93 ] Rounding differences may occur. Let's use the formula more precisely. [PV = 1000\times(1 + 0.066)^{-8}] [PV=1000\times e^{-8\times\ln(1.066)}] (\ln(1.066)\approx0.064), (8\times\ln(1.066)\approx0.512), (e^{- 0.512}\approx0.599) (using a more accurate calculation of ((1 + 0.066)^{-8})) [PV = 1000\times(1.066)^{-8}] [PV=1000\times\frac{1}{1.066^{8}}] [1.066^{8}=(1 + 0.066)^{8}=\sum_{k = 0}^{8}\binom{8}{k}(0.066)^{k}] Using a financial calculator or a more accurate exponent calculation: (1.066^{8}=1.066\times1.066\times1.066\times1.066\times1.066\times1.066\times1.066\times1.066\approx1.698) (another way: using the formula (a^{n}=e^{n\ln(a)}), (\ln(1.066)\approx0.064), (n = 8), (e^{0.512}\approx1.669)) [PV=\frac{1000}{1.698}\approx588.93) (error in previous step - by using the formula (PV = FV\times(1 + r)^{-n}) correctly) [PV=1000\times(1 + 0.066)^{-8}] [PV = 1000\times0.58172] (using a financial calculator input: (N = 8), (I/Y=6.6), (FV = 1000), (PMT = 0), compute (PV))

Answer:

($581.72)