Future Value of Investments The future value FV

Future Value of Investments The future value (FV) is the value of a current asset at a specified date in the future based on an assumed rate of growth over time. FV Video 1

Warm-Up 1. Stacy deposits $4, 025 in a one year CD at 3. 85% interest, compounded daily. What is the annual percentage yield (APY) to the nearest hundredth of a percent? 2. Find the interest earned on a $25, 000 deposited for ten years at 4¼% interest, compounded continuously. 3. Find the interest earned on a $15, 000 deposit for eight months at 4½% interest, compounded continuously. 2

Introduction Time value of $ 3

Vocabulary FUTURE VALUE OF A SINGLE DEPOSIT INVESTMENT: The balance of an account grows to at some point in the future. $ $ $ PERIODIC INVESTMENT: The same deposits made at regular intervals, such as yearly, monthly, biweekly, weekly or even daily. FUTURE VALUE OF A PERIODIC DEPOSIT INVESTMENT: The balance of an account will grow based on periodic investments. 4

Future Value of a Periodic Deposit Investment ( B = balance at end of investment period P = periodic deposit amount ) () r = annual interest rate expressed as decimal n = number of times interest is compounded annually t = length of investment in years 5

EXAMPLE 1 Rich and Laura are both 45 years old. They open an account at the Mission Savings Bank with the hope that it will gain enough interest by their retirement at the age of 65. They deposit $5, 000 each year into an account that pays 4. 5% interest, compounded annually. A. What is the account balance when Rich and Laura retire? 6 Financial Algebra © Cengage Learning/South-Western

EXAMPLE 1 continued. . . Rich and Laura are both 45 years old. They open an account at the Rhinebeck Savings Bank with the hope that it will gain enough interest by their retirement at the age of 65. They deposit $5, 000 each year into an account that pays 4. 5% interest, compounded annually. B. How much more would Rich and Laura have in their account if they decide to hold off retirement for an extra year? B. How much interest will Rich and Laura earn over the 20 year period? 7 Financial Algebra © Cengage Learning/South-Western

EXAMPLE 2 Linda and Rob open an online savings account that has a 3. 6% annual interest rate, compounded monthly. If they deposit $1, 200 every month, how much will be in the account after 10 years? 8 Financial Algebra © Cengage Learning/South-Western

3 -8 Present Value of Investments Present value (PV) is the current worth of a future sum of money or stream of cash flows given a specified rate of return. 9

Vocabulary $ PRESENT VALUE: Current value of a deposit that is made in the present time. $ $ PRESENT VALUE OF A SINGLE DEPOSIT INVESTMENT: how much a one time deposit should earn at a specific interest rate in order to have a certain amount of money saved for a future savings goal. 10

Vocabulary $ PRESENT VALUE OF A PERIODIC DEPOSIT INVESTMENT: How much to save on a regular basis at a specific interest rate to meet that future goal. $ $ 1 1

PV Periodic v. PV Single Present Value Periodic and Present Value Single deposits determine what you need to save now. 12

Present Value of a Single Deposit Investment ( ) B = ending balance P = principal or original balance (present value) r = annual interest rate expressed as decimal n = number of times interest is compounded annually t = number of years 13

EXAMPLE 3 Mr. and Mrs. Johnson know that in 6 years, their daughter Ann will attend State College. She will need about $20, 000 for the first year’s tuition. How much should the Johnsons depositinto an account that yields 5% interest, compounded annually, in order to have that amount? Round your answer to the nearest thousand dollars. 14 Financial Algebra © Cengage Learning/South-Western

EXAMPLE 4 Ritika just graduated from college. She wants $100, 000 in her savings account after 10 years. How much must she deposit in that accountnow at a 3. 8% interest rate, compounded daily, in order to meet that goal? Round up to the nearest dollar. 15 Financial Algebra © Cengage Learning/South-Western

Present Value of a Periodic Deposit Investment ( ( ) B = ending balance P = principal or original balance r = annual interest rate expressed as decimal n = number of times interest is compounded annually t = number of years ) 16

EXAMPLE 5 Nick wants to install central air conditioning in his home in 3 years. He estimates the total cost to be $15, 000. How much must he deposit monthlyinto an account that pays 4% interest, compounded monthly, in order to have enough money? Round up to the nearest hundred dollars. 17 Financial Algebra © Cengage Learning/South-Western

PRACTICE Pg. 159 # 2, 3, 5 -7 Pg. 165 # 4, 7, 8, 9 18 Financial Algebra © Cengage Learning/South-Western