Calculating Present Value

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Part I: A. Suppose your bank account will be worth $15,000.00 in one year. The interest rate (discount rate) that the bank pays is 7%. What is the present value of your bank account today? Present Value = Future Value / ((1 + int. rate)^(time periods)) PV = 15,000 / ((1 + .07)^1) PV = 15,000 / 1.07 $14,018.69 What would the present value of the account be if the discount rate is only 4%? PV = 15,000 / (1+ .04)^1 PV = 15,000 / 1.04 $14,423.77 B. Suppose you have two bank accounts, one called Account A and another Account B. Account A will be worth $6,500.00 in one year. Account B will be worth $12,600.00 in two years. Both accounts earn 6% interest. What is the present value of each of these accounts? Account A Account B PV = 6,500 / ((1+ .06)^1) PV = 12,600 / (1+ .06)^2) PV = 6,500 / 1.06 PV = 12,600 / 1.1236 $6,132.08 $11,213.96 C. Suppose you just inherited a gold mine. This gold mine is believed to have three years worth of gold deposit. Here is how much income this gold mine is projected to bring you each year for the next three years: Year 1: $49,000,000. Year 2: $61,000,000. Year 3: $85,000,000 Present Value of goldmine at 7% discount rate: PV = (49,000 / ((1 + .07)^1)) + (61,000 / ((1 + .07)^2) + (85,000 / ((1 + .07)^3) PV = (49,000 / 1.07) + (61,000 / 1.1449) + (85,000 / 1.22504) PV = 45,794.39 + 53,279.76 + 69,385.49 PV = $168,459.64 Present Value of goldmine at 5% discount rate: PV = (49,000 / ((1 + .05)^1) + (61,000 / ((1 +

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