1. Compound Interest I.. Compound Interest: A = P ( 1 + r/n)nt
A = Account balance after time has passed.
P = Principal: $ you put in the bank.
r = interest rate (written as a decimal).
n = number of times a year the interest is compounded. (annual = 1, semi-annual = 2, quarterly = 4, monthly = 12, etc.)
t = time (in years) the money is in the bank.
A) To determine the Account balance after time has passed, plug all the #s into the formula and simplify.

2. Compound Interest
Examples: 1) If you deposit $4000 in an account that pays 2.92% interest semi-annually, what is the balance after 5 years? How much did the account earn in interest?
A = P ( 1 + r/n )nt  A = ( /2 )2•5
A = ( )10
A = (1.0146)10
A = $
So the account gained $ dollars in the 5 years.

3. Compound Interest
Examples: 2) If you deposit $12,500 in an account that pays 4.5% interest quarterly, what is the balance after 8 years? How much did the account earn in interest?
A = P ( 1 + r/n )nt  A = ( /4 )4•8
A = ( )32
A = ( )32
A = $ 17,880.64
So the account gained $ dollars in the 8 years.

4. Compound Interest
II.. Solving for P in Compound Interest: A = P (1 + r/n)nt
A) Plug all the #s into the formula.
B) Simplify the ( )nt part.
C) Divide both sides by the ( )nt part.

5. Compound Interest
Examples: 3) How much would you have to deposit in a savings CD paying 4.9% annually so that you will have $60,000 in your account after 12 years?
A = P ( 1 + r/n )nt  ,000 = P ( /1 )1•12
60,000 = P ( )12
60,000 = P (1.049)12
(1.049) (1.049)12
P = $ 33,795.20

6. Compound Interest
III.. Solving for r in Compound Interest: A = P (1 + r/n)nt
A) Plug all the #s into the formula.
B) Divide by the P part to get (1 + r/n)nt by itself.
C) Get rid of the exponent with a radical.
1) Use a reciprocal fractional exponent.
D) Evaluate the A/P^(1/nt) term with a calculator.
E) Solve for r.
1) Move the decimal 2 places to get a %.

7. Compound Interest
Examples: 4) Your Great Grandpa bought his bride to be an engagement ring valued at $ back in It was appraised in 2008 as being worth $12, What was the rate of increase per year?
A = P ( 1 + r/n )nt  = 200 ( 1 + r/1 )1•80
12500 = 200 ( 1 + r )80
62.5 = (1 + r )80
62.5^(1/80) = ( 1 + r )80•(1/80)  = 1 + r
(subtract the 1) = r so r = 5.3%