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SOLVING TIME VALUE OF MONEY PROBLEMS I. Single (Annual) Compounding Period Examples A. Future Value (FV) of a Single Current Lump Sum Received One Period Hence FV = PV(1+i) | PV: current (or present) value | | i: a given interest rate (or rate of return) | (If the tables are used, this is the related formula: FV = PV * FVIF Equation 2 in the Week 1 Lecture) Example: You place \$100 today in a bank deposit account that pays 10% annual interest. In other words, interest on your \$100 worth of principal is paid once a year and will be received one year from today. What will your deposit account be a year from today? Algebraically, the relationship is: FV = \$100(1.1) = \$110 Using Excel, try entering the following formula…show more content…
Algebraically: PV = \$100/[1 + .1/2)]2x1 = \$100/[1 + .1/2)]2 = \$90.70 Using Excel, entering the following formula in a single spreadsheet cell will result in a value of 90.70: =100/(1+(.1/2))^2 Now, let's extend the process just described into a multi-period context. If you are to amass \$100 five years from today, you wish to know the amount of funds you would need to place in a bank account today. The account pays 10% annual interest, with this interest compounded semi-annually. Algebraically: PV = \$100/[1 + .1/2)]2x5 = \$100/[1 + .1/2)]10 = \$61.39 Using Excel, entering the following formula in a single spreadsheet cell will result in a value of 61.39: =100/(1+(.1/2))^10 Now, let's consider the future value counterpart of multiple compounding within a given period. The basis for this calculation involves amending the relationship previously identified. The future value of a single current lump sum one period hence is: FV = PV[1+ (i/n)]ny ; where n equals the number of compounding periods during the year and y equals the number of years. For a single year, y = 1. Suppose you want to know how much you will have in one year if today you place \$100 in a bank deposit account that pays 10% annual interest, with interest compounded on a quarterly basis. In this case: FV = \$100[1+ (.1/4)]4x1 = \$100[1+