Please show the formula used. Present Value. What is the present value of a. $45
ID: 2626442 • Letter: P
Question
Please show the formula used.
Present Value. What is the present value of a. $453 to be received 8 years from now at a 14 percent discount rate? b. $1200 to be received 7 years from now at a 12 percent discount rate? Future Value of an Annuity. What is the future value of a. $1321 a year for 13 years at 13 percent compounded annually? b. $867 a year for 10 years at 13 percent compounded annually? Present Value of an Annuity. What is the present value of a. $487 a year for 5 years at a 9 percent discount rate? b. $798 a year for 13 years at a 11 percent discount rate?Explanation / Answer
a) FV = $453 ; n = 8 years ; Discount rate i = 14% = 0.14
PV = FV / (1 + i)n= 453/(1+0.14)8 = $158.803
b) FV = $1200 ; n = 7 years ; Discount rate i = 12% = 0.12
PV = FV / (1 + i)n= 1200/(1+0.12)7 = $542.82
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Future value of int rate factor for an Annuity = [ (1+i)n - 1 ] / i
a) PMT = payment per period = $1321; n = 13 years; Compounding rate = 13% = 0.13
Future value of int rate factor for an Annuuity = [ (1+0.13)13 - 1 ] / 0.13 = 29.985
Future Value = PMT * Future value of int rate factor for an Annuuity
= $1321 * 29.985 = $39609.79
b) PMT = payment per period = $867; n = 10 years; Compounding rate = 13% = 0.13
Future value of int rate factor for an Annuuity = [ (1+0.13)10 - 1 ] / 0.13 = 18.42
Future Value = PMT * Future value of int rate factor for an Annuuity
= $867 * 18.42 = $15969.92
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Present value of int rate factor for an Annuity = [ (1+i)n - 1 ] / [ i * (1 + i)n ]
a) PMT = payment per period = $487; n = 5 years; Compounding rate = 9% = 0.09
Present value of int rate factor for an Annuuity = [ (1+0.09)5 - 1 ] / [0.09*(1+0.09)5 ] = 3.889
Present Value = PMT * Present value of int rate factor for an Annuuity
= $487 * 3.889 = $1894.26
b) PMT = payment per period = $798; n = 13 years; Compounding rate = 11% = 0.11
Present value of int rate factor for an Annuuity = [ (1+0.11)13 - 1 ] / [0.11*(1+0.11)13 ] = 6.749
Present Value = PMT * Present value of int rate factor for an Annuuity
= $798 * 6.749 = $5386.40