The Future Value of a Single Amount - Business Finance - ثاني ثانوي
PART 1
Chapter 1 An Introduction to Basic Finance
Chapter 2 The Role of Financial Markets and Financial Intermediaries
Chapter 3 Analysis of Financial Statements
PART 2
Chapter 4 An Introduction to Financial Markets
Chapter 5 Opportunity Costs and the Time Value of Money
Chapter 6 Risk and Its Measurements
Chapter 7 Stock and Bonds
5.2 The Future Value of a Single Amout Link to digital lesson Key Terms Future value Compounding Money deposited in an investment account will grow as a result of earnings paid to the investor. In various cultures these earnings are referred to as interest or profit rate, resulting in your savings increasing in value. Future value is the amount by which savings will increase based on a certain rate and over a certain time period. FV=PV (1 +) www.lem.edu.sa fume value The amount by which savings will increase based on a certain rate and over a certain time period Where: FV = Future value PV = Present value i = Interest rate n Number of time periods.. The future value of a single amount calculation may be used to: ⚫ Determine the value of savings and investment at a later date. • Grow money to achieve a financial goal. ⚫ Set aside funds by a business to replace equipment or machinery in the future. EXAMPLE What is the future value of a SAR 100 deposited in a 4% account for one year? Future value (FV) = PV (1 + i)" Future Value (FV) = SAR 100 (1+0.04)" Future Value (FV) = SAR 104 وزارة التعليم M CHAPTER Opportunity Costs and the Time Value of Money 195
Key Terms Future value Compounding
Future value
Cainpounding The process by whicveanings are based on the original amount as well as previous amounts earned EXAMPLE If you deposit SAR 1,000 in a 5% account at age 40, how much will you get at age 65? (invested for 25 years) The future value (FV) will be SAR 1,000 (1+0.05)³ FV = SAR 3,386 What if you deposit the same amount of SAR 1,000 in the same 5% account at the early age of 25, how much will you get at age of 65 (invested for 40 years)? The future value (FV) will be SAR 1,000 (1+0.05)* FV - SAR 7,040 If you make deposits at age 25 rather than at age 40, the greater the future value will be. The same deposit made at the age of 25 would give an account balance of SAR 7,040 at age 65 due to the extra 15 years of compounding. Earning interest on interest is called compounding. Money that is deposited in savings accounts is frequently referred to as being compounded because interest is earned on both the original amount and the previously earned interest. Compounding allows the future value of a deposit to grow faster than if interest were paid only on the original deposit. The sooner you make deposits, the greater the future value will be. Why is it a benefit to let your savings compound? 196 tim
EXAMPLE If you deposit SAR 1,000 in a 5% account at age 40, how much will you get at age 65? (invested for 25 years)
Compounding
Why is it a benefit to let your savings compound?
EXAMPLE What is the future value of SAR 100 at 10% after three years? There are three methods to solve this problem; 1. the formula method, 2. the financial calculator method; and 3. the spreadsheet method. Each will give the same answer. Calculations involve the following elements: FV = Future value SAR 100 SAR 1000 101 yem Earnings SAR 10 PV = Present value 1 = Interest rate n = Number of time periods Future value (rounded) SAA 110 SAR 121 SAR 133 SAR 1100 10 year Earnings SAR (SAR 121 0 10 year Earnings SAR 12 2 Years 3 Calculation Methods Using this same example (future value of SAR 100 at 10% after three years), the formula, financial calculator, and spreadsheet calculations are as follows: Future Value of *Single Amount Formula Financial Calculator (Note: Different Financial calculators may require slightly different keystrokes) Spreadsheet Process keystrokes Calculation FV PVT +0 SAR 133 SAR 100 (1-0.10) PV I/YN, PMT CPT FV -100 PV, 10 I/Y 3 N 0 PMT, CPT FV 133 = FV IRATE, NPER, PMT PV, TYPE =FV (0.1,3,0, -100,0) = 133 Note: Financial calculators and spreadsheet software may require you to enter amounts as negative numbers since these are viewed as cash outflows, money that is going into a savings account and investment. The result is a positive number, a cash inflow. وزارة التعليم . 2021-1689 CHAPTER 5 Opportunity Costs and the Time Value of Money 197
What is the future value of SAR 100 at 10% after three years?
. 198Business Finance You Try It Noor invests SAR 700 at 4% for seven years. What would the future value be? Sara Invests SAR 1,000 in 0.6% account for five years. What amount does she receive after five years? All starts two investment accounts, both with SAR 1,000. The first is a 5% account and the second is a 6% account. What is the difference between the account balances after five years! Exercises Choose the correct answer. 1. Which of the following are needed to calculate the future value of an Investment? a. the amount of savings? b. the annual rate? c. length of time the money is on deposit? d. all of the above? 2. What amount will be in an investment account after five years of earning 3% if the starting balance is SAR 1007 a. SAR 114 b. SAR 116 c. SAR 118 d. SAR-110
Noor invests SAR 700 at 4% for seven years. What would the future value be?
Sara invests SAR 1,000 in a 6% account for five years. What amount does she receive after five years?
Ali starts two investment accounts, both with SAR 1,000. The first is a 5% account and the second is a 6% account. What is the difference between the account balances after five years?
Which of the following are needed to calculate the future value of an investment?
What amount will be in an investment account after five years of earning 3% if the starting balance is SAR 100?
