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Compound Interest

Compound Interest. Sum(1/L1). Vocabularies and Symbols. A = Accumulated Amount (ending balance, in $) P = Principal (beginning balance, in $) r = Interest Rate (such as 5%, or 0.05) t = Time (in years). Simple Interest:.

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Compound Interest

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  1. Compound Interest Sum(1/L1)

  2. Vocabularies and Symbols • A = Accumulated Amount (ending balance, in $) • P = Principal (beginning balance, in $) • r = Interest Rate (such as 5%, or 0.05) • t = Time (in years)

  3. Simple Interest: • An 100$ deposit is earning 10% annual simple interest in a saving account. What will be the ending balance after t years, for t = 0, 1, 2, 3 and 4 years? • A(0)=100 • A(1)=110 • A(2)=120 • A(3)=130 • A(4)=140, etc… • Every year, the amount of interest is a constant 10$, which is 10% of P.

  4. Simple vs. Compound Interest

  5. Compound Interest • A = Accumulated Amount • P = Principal • r = Interest Rate • t = Time

  6. Compound Interest • A deposit of $2500 is made in an account that pays an annual interest rate of 5%. Find the balance in the account at the end of 5 years if the interest is: • Simple Interest • Compounded Annually • Compounded Quarterly

  7. Compound Interest • A = Accumulated Amount • P = Principal • r = Interest Rate • t = Time • n = Compounding Frequency (# of times a year. If annually, n=1; if quarterly, n=4, etc.) • Note: • nt = total # of compounding periods • r/n = interest rate earned in each compounding period

  8. Compound Interest • A deposit of $2500 is made in an account that pays an annual interest rate of 5%. Find the balance in the account at the end of 5 years if the interest is: • Simple Interest • Compounded Annually • Compounded Quarterly • Compounded Monthly • Compounded Daily

  9. Continuously Compound • A deposit of $2500 is made in an account that pays an annual interest rate of 5%. Find the balance in the account at the end of 5 years if the interest is: • Compounded CONTINUOUSLY

  10. Continuously Compounded Interest • A = Accumulated Amount • P = Principal • r = Interest Rate • t = Time

  11. Continuously Compound • A deposit of $2500 is made in an account that pays an annual interest rate of 5%. Find the balance in the account at the end of 5 years if the interest is: • Compounded CONTINUOUSLY

  12. Compound Interest • A deposit of $2500 is made in an account that pays an annual interest rate of 5%. Find the balance in the account at the end of 5 years if the interest is: • Simple Interest: $3125 • Compounded Annually: $3190.70 • Compounded Quarterly: $3205.09 • Compounded Monthly: $3208.40 • Compounded Daily: $3210.01 • Compounded Continuously: $3210.06

  13. Interest rate vs. Compounding • P = $2500 • r = 5% • t = 5 years • Compounded daily will give: • $3210.01 • If compounded annually, but raise interest rate to 5.5%, it will give: • $3267.40 • Which is a better deal: compounding more frequently, or raising interest rate?

  14. Don’t be mean to the floop … Tryout for Cheerleading =]

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