Time Value of Money: Calculations for Perpetuities, Annuities, and Future ValueQuestion1What is the value of a perpetuity with an annual payment of $50 and a discount rate of4%?The value ofperpetuity is given by the following formulaValue ofperpetuity = A/rWhere, A = Annual PaymentAnd r = Discount rateSubstituting the values we getValue of perpetuity = $50/0.04= $1250Question 2What is the present value of an annuity with annual payments of $1200, a discount rate of8%, and a duration of 15 years?Thepresentvalue of annuity is given by the following formulaPresent Value of annuity = P[1–{1/(1+r)n}] / rWhere, P= Amount of each paymentr = Discount raten = Number of periodsSubstituting the values we getPresent Value of annuity= $1200 [1–{1/(1+0.08)15}] / 0.08= $10271.37Question 3andQuestion 4What is the future value of an annuity with annual payments of $10,000, a discount rateof 9%, and a duration of 10 years?The future value of annuity is given by thefollowing formulaFuture Value of annuity = P [(1+r)n-1] / rWhere, P = Amount of each paymentr = Discount raten = Number of periodsSubstituting the values we getFuture Value of annuity = $10000 [(1+0.09)10-1] / 0.09= $151929.30Question 5What is the future value of a single amount of $5000 after 11 years, given an interest rateof 6%?The future value of a single amount is given by the following formulaFuture Value of amount = P (1+r)nWhere, P = Amountr = Discount raten = Number of periodsSubstituting the values we getFuture Value of amount = $5000(1+0.06)11= $9491.49Time Value Of Money: Calculations For Perpetuities, Annuities, And Future Value
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