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

5.3 The Future Value of a Series of Amounts (Annuity) Key Term Annuity Link to digital lesson www.dem.edu.sa Instead of a single amount, people often make regular deposits to an investment plan for savings goals or retirement. An annuity is a series of equal, annual payments with a constant rate of return. To determine the future value of these equal yearly deposits, the calculation is called the future value of a series. Annuity A series of equal, annua payments with a constant rate of retur Where (1+0)-1 FV (annuity) = PMT x- i FV (annuity) future value of annuity PMT i n = payment per period = interest rate = number of payments Common uses of the future value of a series of amounts include: ⚫ A student/young professional saving a set amount each year for a future financial goal, such as future education costs or retirement. ⚫ A young entrepreneur setting aside an amount each year to start a small business in four years. ⚫ A business owner creating a fund with annual deposits to expand the company into other countries in the future. What uses can you think of far the unu value and present value calculations? 199

200 Business Finance EXAMPLE What is the future value of three SAR 100 deposits made at the end of each of the next three years, and eaming 10% per year? 0 2 3 +SAR 100 +SAR 100 +SAR 100 Year 3: 100 (1+0.10y=SAR 100 Year 2: 100 (1+0.10)=SAR 110 Year : 1001+0:10 SAR 121 SAR 331 The future value of the series would be SAR 331 based on the total future values of the SAR 100 deposits. The answer can be calculated using the formula, financial calculator, and spreadsheet calculations as shown in the table below: Future Value of a Series of Amounts Process, keystrokes Formula Financial Calculator (Note: Different financial calculators may require slightly different keystrokes) Calculation n+/-1 EV (anmulty) = PMT x 331 100 x- (1-10-1 ото PMT N I/Y PV CPT FV -100 PMT 3 N10 /Y 0 PV CPT FV 331 Spreadsheet = FV IRATE NPER, PMT, PV, TYRE =FV (0 1,3-100,0,0) = 331 Remember, this example assumes that: 1. Each deposit is for the same amount. 2. The rate is the same for each time period. 3. The deposits are made at the end of each time period.

You Try It What amount would Sara have in five years if she invested SAR 1,200 each year at a rate of 3% ? All makes three annual deposits of SAR 500. each earning 5%. What is the future value of the investment? Nora invests SAR 250 each year for six years into her investment account which earns her 6% per year What is her total investment at the end of six years? Exercises Choose the correct answer. 1. Every series of deposits is an annuity. True/False 2. The future value of a series of amounts may be used to calculate the future value of an annuity. True/False وزارة التعليم CHAPTERS Opportunity Costs and the Time Value of Money 201