Section 11.3 Compound Interest

Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Section 11.3

Compound Interest


What You Will Learn

Compound InterestPresent Value

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InvestmentsAn investment is the use of money or capital for income or profit.In a fixed investment, the amount invested as principal is guaranteed and the interest is computed at a fixed rate. In a variable investment, neither the principal nor the the interest is guaranteed.

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Compound Interest

Interest that is computed on the principal and any accumulated interest is called compound interest.

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Compound Interest Formula

A is the amount that accumulates in the account

p is the principalr is the annual interest rate as a decimal

t is the time in yearsn is the number of compound periods per year

A p 1

r

n

nt

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Example 2: Using the Compound Interest FormulaKathy Mowers invested $3000 in a savings account with an interest rate of 1.8% compounded monthly. If Kathy makes no other deposits into this account, determine the amount in the savings account after 2 years.

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Example 2: Using the Compound Interest FormulaSolutionp = $3000, r = 0.018, n =12, t = 2

A p 1

r

n

nt

3000 1

0.018

12

122

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Example 2: Using the Compound Interest FormulaSolution

3000(1 0.0015)122

3000(1.0015)24

3000(1.0366279)

3109.88The amount in the account after 2 years would be about $3109.88.

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Annual Percent Yield

The effective annual yield or annual percentage yield (APY) is the simple interest rate that gives the same amount of interest as a compound rate over the same period of time.

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Present Value Formula

p is the present value, or principal to invest now

A is the amount to be accumulated in the account

r is the annual interest rate as a decimaln is the number of compound periods per year

t is the time in years

p A

1 r

n

nt

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Example 5: Savings for CollegeWill Hunting would like his daughter to attend college in 6 years when she finishes high school. Will would like to invest enough money in a certificate of deposit (CD) now to pay for his daughter’s college expenses. If Will estimates that he will need $30,000 in 6 years, how much should he invest now in a CD that has a rate of 2.5% compounded quarterly?

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Example 5: Savings for CollegeSolution

30,000

(1.00625)24

30,000

1.1612320

25,833.30

Will Hunting needs to invest approximately $25,833.30 now to have $30,000 in 6 years.

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Section 11.3 Compound Interest

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Transcript of Section 11.3 Compound Interest