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8.3 Compound Interest

8.3 Compound Interest. In 1626 Peter Minuit bought Manhattan island For $24 worth of beads, cloth etc. If the value of the land increased at 5% simple interest until 2010, the value would be: 24(1 + .05

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8.3 Compound Interest

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  1. 8.3 Compound Interest

  2. In 1626 Peter Minuit bought Manhattan island For $24 worth of beads, cloth etc. If the value of the land increased at 5% simple interest until 2010, the value would be: 24(1 + .05 đť—‘ 384) = 484.8 The actual value of the land in Manhattan in 2010 was 5 billion. The magic of compound interest can account for the difference.

  3. Compound interest: interest payable on both capital and the accumulated interest. OED With compound interest, interest is paid on the principle and on the interest already earned. If interest is compounded annually, the formula for computing the future value is: A = P(1+ r)t

  4. A = P(1+ r)t If $100 is invested at 4% compounded annually for 10 years, the value at the end of ten years would be: 100(1 + .04)10 = 100(1.04)10 = 148.02 What is the future value of $200 invested at 3% compounded annually for 5 years? 200(1 + .03)5 = 200(1.03)5 = 231.85

  5. The general formula for computing compound interest is: Ais the amount after t years. P is the principal invested. r is the interest rate. n is the number of compounding periods in a year. If you invest $1000 at 4% compounded quarterly for 7 years, how much will you have? = $1321.29

  6. Ais the amount after t years. P is the principal invested. r is the interest rate. n is the number of compounding periods in a year. If you invest $1000 at 4% compounded monthlyfor 7 years, how much will you have? = $1322.51

  7. If you invest $1000 at 4% compounded dailyfor 7 years, how much will you have? = $1323.11 Quarterly compounding will yield $1321.29 Monthly compounding will yield $1322.51 Daily compounding will yield $1323.11

  8. The formula to compute the amount if interest is compounded continuously is: If you invest $1000 at 4% compounded continuouslyfor 7 years, how much will you have? = $1323.13 Quarterly compounding will yield $1321.29 Monthly compounding will yield $1322.51 Daily compounding will yield $1323.11

  9. If you invest $500 at 4% compounded quarterly for 100 years, how much will you have? = $26,762.06

  10. If you invest $500 at 5%compounded quarterly for 100 years, how much will you have? = $71,942

  11. $500 invested at 4% compounded quarterly for 100 years. = $26,762.10 $500 invested at 5% compounded quarterly for 100 years. $500 invested at 6% compounded quarterly for 100 years. = $71,942.04 = $192,924.29

  12. In 1626 Peter Minuit bought Manhattan island For $24 worth of beads, cloth etc. If the value of the land increased at 5% interest compounded annually until 2010, the value would be: 24(1 + .05)384 = 3,287,774,968 Compounding monthly the value would be: $5,027,378,918.03. That is approximately the assessed value of the land in Manhattan.

  13. The present value of money to be received in the future is calculated based on the amount of interest that could be earned if P dollars were invested now. The formula for compound interest can be modified to calculate the present value of money. solve for P What is the present value of $5,000 to be received in seven years if the money could earn 6% compounded quarterly? = $3295.50

  14. What is the present value of $100,000 to be received in twenty years if the money could earn 5% compounded monthly? = $36,864.45

  15. What is the present value of $5,000 to be received in seven years if the money could earn 6% compounded continuously? = $3285.23

  16. The effective rate of interest is the equivalent annual simple rate of interest that would yield the same amount as compounding after one year. $100 invested at 6% compounded quarterly for 1 year. $500 invested at 3% compounded monthly for 1 year. The effective rate of interest is 6.14% = $106.14 = $515.21

  17. The effective rate of interest is the equivalent annual simple rate of interest that would yield the same amount as compounding after one year. $500 invested at 3% compounded monthly for 1 year. = $515.21 The effective rate of interest is 3.04%

  18. The formula for calculating the effective rate or the effective annual yield is: What is the effective annual yield on money invested at 3.75% compounded daily for 1 year. = 0.0382 The effective rate of interest is 3.82%

  19. What is the effective annual yield on money invested at 4.5% compounded monthly for 1 year. = 0.0459 The effective rate of interest is 4.59%

  20. What interest rate will be required if you want to double your money in five years if the money is compounded annually? A will be 2P

  21. What interest rate will be required if you want to triple your money in ten years if the money is compounded daily? A will be 3P

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