1. 3-8 PRESENT VALUE OF INVESTMENTS
Banking
9/21/2018
3-8 PRESENT VALUE OF INVESTMENTS
OBJECTIVES
Calculate the present value of a single deposit investment.
Calculate the present value of a periodic deposit investment.
Chapter 1

2. Key Terms present value present value of a single deposit investment
present value of a periodic deposit investment

3. What large purchases do you see in your future?
How can you determine what you need to invest now to reach a financial goal?
What large purchases do you see in your future?
If you know you will need a specific amount of money in the future, how do you determine how much money to deposit

4. Present Value of a Single Deposit
Formula:
𝑃= 𝐵 1+ 𝑟 𝑛 𝑛𝑡
B = ending balance
P = principal or original balance (present value)
r = interest rate (decimal form)
n = number of times interest compounded annually
t = number of years

5. Example 1
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 deposit into an account that yields 5% interest, compounded annually, in order to have that amount? Round your answer to the nearest thousand dollars.
𝑃= ≈$14,924.31→$𝟏𝟓,𝟎𝟎𝟎

6. CHECK YOUR UNDERSTANDING
How many years would it take for $10,000 to grow to $20,000 in the same account? Use a natural logarithm to solve.
𝑃= 𝐵 1+ 𝑟 𝑛 𝑛𝑡 = 𝑡
(n=1)

7. Example 2
Ritika just graduated from college. She wants $100,000 in her savings account after 10 years. How much must she deposit in that account now at a 3.8% interest rate, compounded daily, in order to meet that goal? Round up to the nearest dollar.
𝑃= 𝐵 1+ 𝑟 𝑛 𝑛𝑡 = ≈$𝟔𝟖,𝟑𝟖𝟖

8. CHECK YOUR UNDERSTANDING
How does the equation from Example 2 change if the interest is compounded weekly?
≈$𝟔𝟖,𝟑𝟗𝟔

9. Present Value of a Periodic Investment
Formula: 𝑃= 𝐵× 𝑟 𝑛 1+ 𝑟 𝑛 𝑛𝑡 −1 Variables have the same meanings.

10. EXAMPLE 3
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 monthly into an account that pays 4% interest, compounded monthly, in order to have enough money? Round up to the nearest hundred dollars.
𝑃= 𝐵× 𝑟 𝑛 𝑟 𝑛 𝑛𝑡 −1 = × −1 ≈$392.86
$𝟒𝟎𝟎

11. EXAMPLE 4
Randy wants to have saved a total of $200,000 by some point in the future. He is willing to set up a direct deposit account with a 4.5% APR, compounded monthly, but is unsure of how much to periodically deposit for varying lengths of time. Graph a present value function to show the present values for Randy’s situation from 12 months to 240 months.
𝑃= 𝐵× 𝑟 𝑛 𝑟 𝑛 𝑛𝑡 −1 = × 𝑥 −1

12. 𝑃= 𝐵× 𝑟 𝑛 𝑟 𝑛 𝑛𝑡 −1 = × 𝑥 −1

13. CHECK YOUR UNDERSTANDING
Use the graph to estimate how much to deposit each month for 1 year, 10 years, and 20 years.