# Math Questions on Deriving the Present Value

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1. If my account pays 5% and will be worth \$4200 in one year, the present value of my account today is: 4200 / 1.05 = \$4000 This is a basic calculation. The total one year in the future is derived from the present value today, plus the interest that will be earned over the course of the next year. The interest rate has been established at 5%. All that needs to be done is perform a little algebra and solve the problem for the present value. This leaves us with the formula of future value / interest rate = present value. 2. The present value of the first account will be 3800 / 1.05 = \$3619.05. The present value of the second account will be \$6500 / (1.05)(1.05) = \$5895.69. The combined value of the two accounts is 3619.05 + 5895.69 = \$9514.74. For this question, the same technique is used as was used in the first question. The future value and the interest rate are known, so the equation must be solved for the present value. Then, the present value of both of these figures will be added together. 3. The present value of the oil well's income stream at a 7% discount rate is: Year 1 2 3 Cash Flow 125000 258000 310000 PV 116822.4 225347.2 253052.3 NPV 595222 d 0.07 So the net present value is \$595,222.00 For this equation, I used Excel to calculate the NPV. The formula for NPV is to take the future cash flow and discount it back as follow: PV = FV / (1+d)^t where d = discount rate and t = number of time periods. The three PV values