1. Find the present value of $800 due in the future under each of these conditions:
5% nominal rate, semiannual compounding, discounted back 5
years. Do not round intermediate calculations. Round your answer to
the nearest cent.
$
5% nominal rate, quarterly compounding, discounted back 5 years.
Do not round intermediate calculations. Round your answer to the
nearest cent.
$
5% nominal rate, monthly compounding, discounted back 1 year. Do not round intermediate calculations. Round your answer to the nearest cent.
a)
Rate = 5% / 2 = 2.5%
Number of periods = 5 * 2 = 10
Present value = Future value / (1 + r)^{n}
Present value = 800 / (1 + 0.025)^{10}
Present value = 800 / 1.280085
Present value = $624.96
b)
Rate = 5% / 4 = 1.25%
Number of periods = 5 * 4 = 20
Present value = Future value / (1 + r)^{n}
Present value = 800 / (1 + 0.0125)^{20}
Present value = 800 / 1.282037
Present value = $624.01
c)
Rate = 5% / 12 = 0.4167%
Number of periods = 1 * 12 = 12
Present value = Future value / (1 + r)^{n}
Present value = 800 / (1 + 0.004167)^{12}
Present value = 800 / 1.0511661
Present value = $761.06
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