Name Notes - Savings & Annuities I. Savings et P be the principal amount, or original amount invested at r interest rate, converted to a decimal, compounded once a year. When the interest is added at the end of the year, the new balance will be P1, where P1 = P + Pr = P(1+r). This pattern of multiplying the previous balance by (1+r) is then repeated each successive year. et's make a chart to see the pattern and determine a formula no matter how many years our money is in the bank: Time in years Balance after each compounding To accommodate more frequent compounding of interest, like quarterly, monthly, weekly, or daily, let n be the number of compoundings per year and let t be the number of years. Then the interest rate per compounding period is -, the total times the interest will be compounded is nt, and the balance in the account after t years is A = P(1+3). Examples: 1) Suppose you started a savings account when you were 5 years old with $100, but you never added any more money to it. How much money is in your savings account now if you were getting 3% interest compounded quarterly? 2a) Suppose you started a savings account on your 18th birthday with $1000. How long would it take to double your money if the interest rate was 5% compounded monthly and you never added any more money to the account? (prior knowledge of solving exponential and logarithmic equations is required)