Page 512 - Basic College Mathematics with Early Integers

S E C T I O N 6.6 I PERCENT AND PROBLEM SOLVING: INTEREST 489

interest is added to the principal at the end of each year and that next year’s interest
is computed on this new amount. In this section, we round dollar amounts to the
nearest cent.

Amount at
Beginning
of Year Principal # Rate # Time Interest Amount at End of Year
1st year $2000 $2000 # 0.07 # 1 = $140 $2000 + 140 = $2140

2nd year $2140 $2140 # 0.07 # 1 = $149.80 $2140 + 149.80 = $2289.80
3rd year $2289.80 $2289.80 # 0.07 # 1 L $160.29 $2289.80 + 160.29 = $2450.09

The compound interest earned can be found by

total amount - original principal = compound interest
$2450.09 - $2000 = $450.09
T
T
T
The simple interest earned would have been

principal # rate # time = interest
T T T T
#
#
$2000 0.07 3 = $420
Since compound interest earns “interest on interest,” compound interest earns
more than simple interest.
Computing compound interest using the method above can be tedious. We can
use a calculator and the compound interest formula below to compute compound
interest more quickly.

Compound Interest Formula
The total amount A in an account is given by

r n # t
A = Pa1 + b
n
where P is the principal, r is the interest rate written as a decimal, t is the length
of time in years, and n is the number of times compounded per year.

Example 4 Finding the Total Amount of an Investment PRACTICE 4
$3000 is invested at 4% interest
$1800 is invested at 2% interest compounded annually. Find the total amount after compounded annually. Find the
3 years. total amount after 6 years.
Solution: “Compounded annually” means 1 time a year, so

n = 1. Also, P = $1800, r = 2% = 0.02, and t = 3 years.
r n # t
A = Pa1 + b
n
#
0.02 1 3 Remember order of
= 1800a1 + b operations. First evaluate (1.02) 3 ,
1
then multiply by 1800.
= 1800(1.02) 3
L 1910.17 Round to 2 decimal places.
The total amount at the end of 3 years is $1910.17.
Answer
Work Practice 4 4. $3795.96