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.

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 = 4000 ( 1 + .0292/2 )2•5 A = 4000 ( 1 + .0146 )10 A = 4000 (1.0146)10 A = $ 4623.90 So the account gained $623.90 dollars in the 5 years.

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 = 12500 ( 1 + .045/4 )4•8 A = 12500 ( 1 + .01125 )32 A = 12500 (1.01125)32 A = $ 17,880.64 So the account gained $5380.64 dollars in the 8 years.

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.

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  60,000 = P ( 1 + .049/1 )1•12 60,000 = P ( 1 + .049 )12 60,000 = P (1.049)12 (1.049)12 (1.049)12 P = $ 33,795.20

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 %.

Compound Interest Examples: 4) Your Great Grandpa bought his bride to be an engagement ring valued at $200.00 back in 1928. It was appraised in 2008 as being worth $12,500.00. What was the rate of increase per year? A = P ( 1 + r/n )nt  12500 = 200 ( 1 + r/1 )1•80 12500 = 200 ( 1 + r )80 200 200 62.5 = (1 + r )80 62.5^(1/80) = ( 1 + r )80•(1/80)  1.053 = 1 + r (subtract the 1) .053 = r so r = 5.3%