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3.5 Compound Interest Formula • Imagine you deposit $10,000 in a five-year cd. The account pays 5.2% interested compounded daily. How much will your $10,000 investment be worth by the end of the 5 years? Compound Interest Formula r B p 1 n n t B = ending balance p = principal r = interest rate n = number of compounds per year t = time (in years) Number of Compounds • Annually • n=1 • Semiannually • n=2 • Quarterly • n=4 • Daily • n = 365 (or 366 in a leap year) Marie deposits $1,650 for three years at 3% interest, compounded daily. What is her ending balance? n t r B p 1 n 365 3 p = $1,650 B 1,6501 0.03 365 r = 0.03 n = 365 t=3 B $1,805.38 Kate deposits $2,350 in an account that earns interest at a rate of 3.1%, compounded monthly. What is her ending balance after 5 years? n t r B p 1 n 12 5 p = $2,350 B 2,3501 0.031 12 r = 0.031 n = 12 t=5 B $2,743.45 3.5 Compound Interest Formula APR vs. APY • APR – Annual interest rate • APY – Actual rate you earn with compounding interest Ending Balance- StartingBalance – To find APY: StartingBalance Sharon deposits $8,000 in a one year CD at 3.2% interest, compounded daily. What is Sharon’s APY? n t $8,260.13- $8,000 r APY B p 1 $8,000 n 365 1 0.032 B 8,0001 APY 3.25% 365 B $8,260.13 Barbara deposits $3,000 in a one year CD at 4.1% interest, compounded daily. What is her APY for the account? n t $3,125.55- $3,000 r APY B p 1 $3,000 n 365 1 0.041 B 3,0001 APY 4.19% 365 B $3,125.55