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# (Present value) What is the present value of the following

(Present value) What is the present value of the following future amounts?
a. \$800 to be received 10 years from now discounted back to the present at 10 percent
(Present value of an annuity) What is the present value of the following annuities?
a. \$2,500 a year for 10 years discounted back to the present at 7 percent

The formula for present value of compound interest is

Present value = Future amount (1 + Discount rate) ^ -Number of periods

i.e.

PV = 800 X (1+10)^-10

PV= \$ 308.4

The formula for Present value of Annuity is

PV of Annuity = annuity payment X (1 - (1 + Discount rate)^ -number of period) / Discount rate)

therefore PV = 2,500 X (1-(1+7%) ^ -10) / 7%

PV of Annuity = \$ 17,558.95