Present Value of Investments

Section 3.8

Think about this…

What large purchases or expenditures do you foresee in your future?

How are you preparing to make these purchases a reality?

So far:

We have been calculating how much interest a certain amount of money will make over a given time period at different interest rates & compounding rates.

This is considered the future value of an investment

Next: We want to know how much we need

to invest today to reach a specific amount in a specific amount of time.

This is called the present value of an investment.

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Deposit $1,000 into an account that earns 5% simple interest for 5 years. How much is in the account at the end of those 5 years?

You want to buy a house in 10 years. You estimate that you will need $100,000 for a down payment. If you are going to put your money in an account earning 5% interest, how much should you deposit?

2011 Toyota Camry

Starting price of $20,000

2011 Toyota Camry The Toyota Camry has a starting price

of $20,000. You want to purchase a similar car after college graduation.

If you were going to save some money specifically for the car, what would the best type of account be?

How much do you need to save?

Present Value of a Future Investment

What was our formula for compound interest?

B = P (1 + )rn

nt

(1 + )rn

nt (1 + )

rn

nt

Present Value of a Future Investment

P = (1 + )

rn

ntB

2011 Camry

Starting at $20,000 A 5-year CD has an interest rate of 4%

compounded annually How much do you need to deposit in

the CD to pay for the car in full in 5 years?

??? r = .04 t = 5 B = $20,000

n = 1

P =

(1 + )rn

ntB

r = .04 t = 5 B = $20,000

P =

n = 1

(1 + ).04

1(1x 5)

20,000P = = $16,438.54

2011 Camry

Cost of $20,000

By putting your money in a 5-year CD, you can purchase this car for a price of $16,438.54.

How much do you save?

After College

Looking ahead to your post-college life, you set a goal of having $100,000 in your savings account 10 years after you graduate. How much do you need to deposit in an account that earns 4.5% interest, compounded daily, to meet your goal?

After College

B = $100,000

t = 14 years

r = 0.045n = 365

(1 + )rn

ntB

P =

(1+ )0.045365

(365 x 14)100,000

P =

100,000P =

1.877538

$53,261.25P =

Buying a Condo

You figure that it would make sense to purchase a condo within 3 years of your college graduation. You want to have a minimum of $35,000 for a down payment. If you are going to put this money in a savings account that earns 5.4% interest, compounded monthly, how much money should you deposit?

Buying a Condo

B = $35,000t = 7 yearsr = 0.054n = 12

(1 + )

rn

ntB

P =

(1+ )

0.05412

(12 x 7)

35,000P =

100,000P = 1.458126

$24,003.41P =