Page 807 - Algebra 1

Application: Retirement Investments
Two people plan to retire at age 65. A 25-year-old woman invests $2000 in a bond that pays 7% per year, compounded annually. A 45-year-old man invests $5000 in a bond that pays 7% per year, also compounded annually. Whose investment will be worth more when they reach retirement age and by how much?
SOLUTION
Use A = P(1 + r)t to calculate the value of the investment for each person. For the 25-year-old woman, P = 2000, r = 0.07, and t = 40.
Example
4
Math Reasoning
Analyze Why was the man’s account value less than the woman’s?
A = 2000(1 + 0.07)40
A = 2000(1.07)40
A = 29,948.92
The total value of her account will be $29,948.92.
For the 45-year-old man, P = 5000, r = 0.07, and t = 20.
A = 5000(1 + 0.07)20 A = 5000(1.07)20
A = 19,348.42
Substitute.
Add inside the parentheses.
Simplify using the order of operations.
Substitute.
Add inside the parentheses.
Simplify using the order of operations.
The total value of his account will be $19,348.42. The woman’s investment will be worth $10,600.50 more.
Lesson Practice
a.
(Ex 1)
b.
(Ex 1)
c.
(Ex 1)
d.
(Ex 1)
e.
(Ex 2)
f.
(Ex 2)
g.
(Ex 3)
An account is opened with $5600. The bank pays 4% simple interest annually. How much interest will be earned in 10 years?
$25,000 is invested for 12 years at 6% simple interest. How much will be in the account after 12 years?
$4500 is borrowed at 2.5% simple interest. The total amount of interest paid is $562.50. For how many years was the money borrowed?
After 15 months, $130 had been earned on a $2600 investment. What was the interest rate?
$12,000 is invested at 4% compounded annually. Find the value of the investment after 30 years.
$12,000 is invested at 4% compounded quarterly. Find the value of the investment after 30 years.
An account has $2500 and earns 12% simple interest. Complete the table to find the total amount in the account after 1, 2, 5, and 10 years.
Years
Prt = I
Total Amount in Account
1
2
5
10
792 Saxon Algebra 1