21. Find the present values of these ordinary annuities. Discounting occurs once a year. a. $400 per year for 10 years at 10%. b. $200 per year for 5 years at 5% c. $400 per year for 5 years at 0% d. Rework parts a-c assuming they are annuities due.

a.

PV = $2457.826842 rounded off to $2457.83

b.

PV = $865.8953341 rounded off to $865.90

c.

PV = $400

d.

PV = $2703.609527 rounded off to $2703.61

PV = $909.1901008 rounded off to $909.19

PV = $400

Explanation:

An annuity is a series of cash flows that are constant, that occur after equal interval of time and that are for a defined period of time.

An ordinary annuity is the one whose cash flows occur at the end of the period. While an annuity due is the one whose cash flows occur at the start of the period. The formula for the present value of both the ordinary and the due annuity are attached.

a.

PV = 400 * [(1 - (1+0.1)^-10) / 0.1]

PV = $2457.826842 rounded off to $2457.83

b.

PV = 200 * [(1 - (1+0.05)^-5) / 0.05]

PV = $865.8953341 rounded off to $865.90

c.

PV = 400 * [(1 - (1+0.0)^-5) / 0.0]

PV = $400

d.

PV = 400 * [(1 - (1+0.1)^-10) / 0.1] * (1+0.1)

PV = $2703.609527 rounded off to $2703.61

PV = 200 * [(1 - (1+0.05)^-5) / 0.05] * (1+0.05)

PV = $909.1901008 rounded off to $909.19

PV = 400 * [(1 - (1+0.1)^-10) / 0.1]

PV = $400

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