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Compound growth of savings or investments

Compound growth of savings or investments. Interest: definition. A. a sum paid or charged for the use of money or for borrowing money B. such a sum expressed as a percentage of money borrowed to be paid over a given period, usually one year. Source: dictionary.com. Two types of interest.

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Compound growth of savings or investments

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  1. Compound growth of savings or investments

  2. Interest: definition • A. a sum paid or charged for the use of money or for borrowing money • B. such a sum expressed as a percentage of money borrowed to be paid over a given period, usually one year. Source: dictionary.com

  3. Two types of interest • Simple interest: Fixed percentage of original amount invested or deposited. • Compound interest: Fixed percentage of original amount plus accumulated interest.

  4. Example: $1000 invested at 10%

  5. Simple v. compound • Simple interest = linear growth • Compound interest = exponential growth

  6. Definitions: • Balance: the current value of an account; equivalent to Y in exponential growth formula • Principle: initial amount invested or deposited; equivalent to X in exponential growth formula

  7. Basic formula for compound growth Balance=Principle(1+r)y Where: y = number of time periods of growth r= interest rate or rate of return (percentage expressed as decimal)

  8. Solving for principle Balance/(1+r)y = Principle

  9. Solving for y log (Balance/Principle)/log(1+r) = y

  10. Solving for r ((Balance/principle)^(1/y))-1 = r

  11. Compounding more than yearly Balance=Principle (1+r/n)yn

  12. Compounding quarterly Balance=Principle (1+r/4)4y

  13. Compounding monthly Balance=Principle (1+r/12)12y

  14. 5% APR, compounded quarterly, for 7 years Balance=Principle (1+.05/4)28

  15. 5% APR, compounded monthly, for 7 years Balance=Principle (1+.05/12)84

  16. Annual percentage yield [APY] • In formulas, r was annual percentage rate or APR • When interest gets compounded more often than once per year, actual interest earned in a year is greater than APR

  17. Example: $10,000 invested for 10 years at 8% APR Annually: $21,589.25 Quarterly: $22,080.40 Monthly: $22,196.40

  18. Computing APY • Compute the balance for two consecutive years at comparable point in time. • Calculate percentage change: (new balance-old balance)/old balance

  19. Demonstration Chart to simulate growth in value of: • $10,000 investment • at 3% APR • compounded monthly Open Excel file

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