Future Value = Present Value (1 + r) t in which r is the rate and t is time (MyAccountingCourse, 2016)
Calculation of present value for each option
Present Value (PV) for option A is $10,000
Present Value for OPTION B is FV/ (1+r) t
PV = (20000/(1.065) 10
Calculation of future value for each option
Future value = Present Value (1+r) t
FV = $10000(1.065) 10
Future Value (FV) for option B is $20,000
Based on the calculations, PV of A = $10,000; PV of B = $10,654.50; FV of A = $18,771.40; FV of B = $20,000. Looking at both the present and future values, option B offers the best choice. It is important to note that while calculating the present values and future values, the involved process is an inverse of the other (Dworsky, 2009); thus, choosing between the two lump sums based on the present values often give similar result as choosing between similar two lump sums based on the future values.
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Dworsky, L. N. (2009). Understanding the mathematics of personal finance: An introduction to financial literacy . Hoboken, NJ: Wiley.
MyAccountingCourse. (2016). Present Value. Retrieved April 14, 2017, from www.myaccountingcourse.com/financial-ratios/present-value