compound interest 8.2 part 2. compound interest a = final amount p = principal (initial amount) r =...
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Compound Interest
8.2 Part 2
Compound Interest
• A = final amount
• P = principal (initial amount)
• r = annual interest rate (as a decimal)
• n = number of times compounded per year
• t = number of years
1nt
rA P
n
Example 1:Write an exponential equation to model the growth function in
the situation and then solve the problem.
Suppose you invested $1000 at 5% interest compounded annually (once per year). How much will you have in 10 years?
1nt
rA P
n
1(10).05
1000 11
A
•A = final amount
•P = principal (start) = 1000
•r = annual interest rate = 5%
•n = number of times compounded per year = 1
•t = number of years = 10
Example 1:Write an exponential equation to model the growth function in
the situation and then solve the problem.
Suppose you invested $1000 at 5% interest compounded annually (once per year). How much will you have in 10 years?
1nt
rA P
n
1(10).05
1000 11
A
(10)1000 1.05A
A = 1628.895 = $1628.90
Number of times compounded:
Annually: n = 1
Bi-annually: n = 2
Quarterly: n = 4
Monthly: n = 12
Weekly: n = 52
Daily: n = 365
Example 2:Write an exponential equation to model the growth function in
the situation and then solve the problem. Suppose you invested the same $1000 at 5% interest, but instead of annually the interest is compounded quarterly (4 times a year)? Now how much will you have in 10 years?
1nt
rA P
n
4(10).05
1000 14
A
•A = final amount
•P = principal (start) = 1000
•r = annual interest rate = 5%
•n = number of times compounded per year = 4
•t = number of years = 10
Example 2:Write an exponential equation to model the growth function in
the situation and then solve the problem. Suppose you invested the same $1000 at 5%
interest, but instead of annually the interest is compounded quarterly (4 times a year)? Now how much will you have in 10 years?
1nt
rA P
n
(40)1000 1.013A
A = 1643.619 = $1643.62
4(10).05
1000 14
A
Compounded annually:$1628.90
Example 3:Write an exponential equation to model the growth function in
the situation and then solve the problem.
Suppose you invested the $1000 at 5% interest, but now your interest is compounded daily. How much will you have in 10 years?
1nt
rA P
n
365(10).05
1000 1365
A
•A = final amount
•P = principal (start) = 1000
•r = annual interest rate = 5%
•n = number of times compounded per year = 365
•t = number of years = 10
Example 3:Write an exponential equation to model the growth function in
the situation and then solve the problem.
Suppose you invested the $1000 at 5% interest, but now your interest is compounded daily. How much will you have in 10 years?
1nt
rA P
n
A = 1648.665 = $1648.67
365(10).05
1000 1365
A
Compounded quarterly:$1643.62
Solve the following problems on a separate piece of paper. Set up the equation first!
You may work with ONE other person.When you finish, you may turn in your work.You may use a calculator.
1) Suppose you invested $2000 at 6% interest, compounded monthly. How much will you have in 10 years?
2) Suppose you invested $500 at 4% interest, compounded bi-annually. How much will you have in 25 years?
Homework: page 370-372 (2-14 evens, 19-21 all, 31-34 all)