The Present Value of a Series of Amounts Annuity - Business Finance - ثاني ثانوي

5.5 The Present Value of a Series of Amounts (Annuity) A person may wish to withdraw an amount each year for a certain number of years. To determine how much must be deposited now, the calculation involves the present value of a series (annuity). Where: PV (annuity) = PMT X- T 1- (1+)m PV (annuity) = present value of annuity PMT i n payment per period = interest rate = number of payments The present value of a series of amounts may be used for: ⚫ Setting up a fund in which a person could withdraw funds, to cover living expenses while in school. ⚫ Making a current deposit to withdraw funds each year to update a school's computers. ⚫ Creating a company fund that would allow an amount to be withdrawn each year to provide employees with advanced training. وزارة التعليم -1 www.imm.edu CHAPTER Opportunity Costs and the Time Value of Money 205

206ly Business Finance EXAMPLE What is the present value of a SAR 100 withdrawal at the end of the next three years for money earning 10%? Present value (fund balance) 0 2 3 -SAR 100 -SAH 100 -SAR 100 100 Year = SAR 91 (1+0.10)' Year 2: 100 (1+010 = SAR 83 100 Year 3 =SAR 75 11+010 5AR 249 Year end The present value of a SAR 100 withdrawal at the end of the next three years would be SAR 249. Using this same example, the calculations are as follows: Present Väling of Formula (1+0.101 PV (annuity) PMT < 249 100 x 0.10 Financial Calculator [Note: Different financial calculators may require slightly different keystrokes) Spreadsheet PMT CPT PV NIYEV -100 PMT N,10 MY 0 FV CPT PV 249 PV (RATE NPER, PMT, EV, TYPE) PV (0.1,3-100,0,0)=249

You Try It How much must Omer deposit today if he wants to take SAR 400 out of an investment account each year for nine years for money earning an annual rate of 8%! If All needs to withdraw SAR 100 every year for five years from an account that earns 6%, how much does he need to invest now! If Sara needs to withdraw SAR 250 every year for seven years and the account eams 7%, how much must she invest now? وزارة التعليم CHAPTER 3 Opportunity Costs and the Time Value of Money 207

. 208Business Finance Exercises Choose the correct answer. 1. Present value of a series may be used by a person who wants to withdraw an amount each year for a certain number of years. True/False 2. The present value of a series requires calculating the amount set aside today to allow regular future withdrawals. True/False