Page 513 - Basic College Mathematics with Early Integers

490 C HAPTE R 6 I PERCENT

PRACTICE 5 Example 5 Finding Total Amount Received from an Investment
1
$5500 is invested at 6 %
4 $4000 is invested at 5.3% compounded quarterly for 10 years. Find the total
compounded daily
for 5 years. Find the total amount at the end of 10 years.
amount at the end of 5 years. Solution: “Compounded quarterly” means 4 times a year, so
(Use 1 year = 365 days .)
n = 4. Also, P = $4000, r = 5.3% = 0.053, and t = 10 years.
r n# t
A = Pa1 + b
n
0.053 4 # 10
= 4000a1 + b
4
= 4000(1.01325) 40
L 6772.12

The total amount after 10 years is $6772.12.
Work Practice 5

r n . t
Note: Part of the compound interest formula, a1 + b , is called the compound
n
interest factor. Appendix A.7 contains a table of various calculated compound inter-
est factors. Another way to calculate the total amount, A, in the compound interest
formula is to multiply the principal, P, by the appropriate compound interest factor
found in Appendix A.7.
The Calculator Explorations box on the next page shows how compound interest
factors are calculated.

Objective Calculating a Monthly Payment

We conclude this section with a method to find the monthly payment on a loan.

Finding the Monthly Payment of a Loan
principal + interest
monthly payment =
total number of payments

PRACTICE 6 Example 6 Finding a Monthly Payment
Find the monthly payment on a
Find the monthly payment on a $2000 loan for 2 years. The interest on the 2-year
$3000 3-year loan if the interest
loan is $435.88.
on the loan is $1123.58.
Solution: First we determine the total number of monthly payments.The loan is
#
for 2 years. Since there are 12 months per year, the number of payments is 2 12, or
24. Now we calculate the monthly payment.
principal+interest
monthly payment =
total number of payments

monthly payment = $2000+$435.88
24
≠$101.50 Copyright 2012 Pearson Education, Inc.
The monthly payment is about $101.50.
Answers
Work Practice 6
5. $7517.41 6. $114.54