Page 805 - Algebra 1

790 Saxon Algebra 1
The amount in an account grows faster with compound interest. Compound interest is interest that is paid on both principal and on previously-earned interest. The compound interest formula gives the total amount accumulated after a given number of years.
Compound Interest Formula
A = P(1 + _r )nt n
A
the total amount after t years
P
the principal
r
the annual rate, a percent expressed as a decimal
t
the time in years
n
the number of times interest is compounded each year
Finding Compound Interest
a. $5000 is invested at 6% compounded annually. Find the value of the investment after 10 years.
SOLUTION
The principal P is 5000. The rate r is 6% or 0.06. The time t is 10 years.
Example
2
Math Reasoning
Justify Explain why the formula for interest compounded annually is A = P(1 + r)t.
A = P(1 + r)t
= 5000 · (1 + 0.06)10 = 5000 · (1.06)10
= 5000 · 1.790847697 = 8954.24
Write the formula, then evaluate. Substitute the values of the variables. Simplify inside the parentheses.
Simplify the power, and do not round. Multiply, and round to the nearest penny.
The value of the investment will be $8954.24.
b. $5000 is invested at 6% compounded quarterly. Find the value of the investment after 10 years.
SOLUTION
The principal P is 5000. The rate r is 6% or 0.06. The time t is 10 years and n = 4 because quarterly means four times per year.
Hint
Use a calculator to evaluate the power and to multiply the result by the principal.
A = P(1 + _r )nt
Write the formula, then evaluate.
Substitute the values of the variables.
Use the order of operations to simplify. Simplify the power and do not round. Multiply and round to the nearest penny.
(
n
_0.06 )4(10) =50001+ 4
= 5000 · (1.015)40
= 5000 · 1.814018409 = 9070.09
The value of the investment will be $9070.09.