2-5 Compound Interest Formula

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Presentation transcript:

2-5 Compound Interest Formula Advanced Financial Algebra

What is compound interest? Remember description and examples from Section 2-4. Compound interest means that you are paid interest on your balance AND on previous interest you have earned. Compound interest allows your money to grow FASTER!

Developing formula Start with % increase and decrease formula: A = P (1+𝑟) 𝑡 = Principal (1+𝑟𝑎𝑡𝑒) 𝑡𝑖𝑚𝑒 r is the interest rate, but we must divide it into periods depending upon how frequent compounding occurs: r = %/(# of compounds per year, n) written as a decimal Periodic compounding formula (not just yearly/annual): A = P (𝟏+ 𝒓 𝒏 ) (𝒏𝒕) A = amount $ after time P = Principal (original $) r = rate as a decimal n = number of compounds per year t = time in years

Example 1 – quarterly compounding using formula Jose opens a savings account with principal P dollars that pays 2% interest, compounded quarterly. What will his ending balance be after 1 year? SOLUTION: Use the formula: A = P (1+ 𝑟 𝑛 ) (𝑛𝑡) = P (1+ .02 4 ) (4∗1) = P (𝟏.𝟎𝟎𝟓) (𝟒)

Example 2 – daily compounding using formula If you deposit P dollars for 1 year at 2.3% compounded daily, express the ending balance algebraically. SOLUTION: Use the formula with r = 2.3% as a decimal = .023 and n = 365 for daily: A = P (1+ 𝑟 𝑛 ) (𝑛𝑡) = P (1+ .023 365 ) (365∗1) = P (𝟏.𝟎𝟎𝟎𝟎𝟔𝟑𝟎𝟏𝟒) (𝟑𝟔𝟓)

Example 3 – daily compounding given Principal Marie deposits $1,650 for 3 years at 1% interest, compounded daily. What is her ending balance? SOLUTION: Use the formula with P = $1.650, r = 1% as a decimal = .01, n = 365 for daily, and t = 3 years: A = P (1+ 𝑟 𝑛 ) (𝑛𝑡) = 1650 (1+ .01 365 ) (365∗3) = $1,700.25 after three years

Assignment: pg 100 #3-6, 8, 11, 13 #3 #4 #5

Assignment: pg 100 #3-6, 8, 11, 13 continued #6 #8 #11 #13 Rodney invests a sum of money, P, into an account that earns interest at a rate of r, compounded yearly. Gerald invests half that amount P/2 into an account that pays twice Rodney’s interest rate 2r. Which of the accounts will have the higher ending balance after 1 year? Explain.