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Compound Interest Equation A = P(1+ )n•t Continuous Compounding n r Continuous Compounding A = Per•t A comparison question relating quarterly compounding to continuous compounding. If you invest $2,000 at an annual interest rate of 9% compounded quarterly, calculate the finalamount you will have in he account after 20 years. P=$2000, r = 0.09, n=4, t=20 A = 2000(1+ )4•20 A = $11,860.29 Compound Interest Equation 0.09 Continuous Compounding 4 If you invest $2,000 at an annual interest rate of 9% compounded continuously, calculate the final amount you will have in he account after 20 years. P=$2000, r = 0.09, t=20 A = 2000e0.09•20 A = $12,099.29 Continuous Compounding more!! Answer (to the nearest dollar): $ If you invest $1,000 at an annual interest rate of 5% compounded continuously, calculate the final amount you will have in the account after 5 years. P = r = t = in years as a decimal with a leading zero: 5% written as 0.05 no commas or $ Continuous Compounding A = Per•t Assume you invest $5,000 in an account paying 8% interest compounded continuously. How much money will be in the account after 5 years? Answer (to the nearest dollar): $ P = r = t = in years as a decimal with a leading zero: 5% written as 0.05 no commas or $ Continuous Compounding A = Per•t Find the amount of money you will have after 10 years if $15,000 is invested in accounts paying 6% interest compounded continuously. Answer (to the nearest dollar): $ P = r = t = in years as a decimal no commas or $ Continuous Compounding A = Per•t Find the amount of money in the account after 18 years if Rebecca invested $15,000 into an account that pays 10% interest compounded continuously. Answer (to the nearest dollar): $ P = r = t = in years as a decimal with a leading zero: 5% written as 0.05 no commas or $ Continuous Compounding A = Per•t How much money will you have if you invest $4000 in a bank for sixty years at an annual interest rate of 9%, compounded continuously? Answer (to the nearest dollar): $ P = r = t = in years as a decimal with a leading zero: 5% written as 0.05 no commas or $ Continuous Compounding A = Per•t Find the amount of money you will have after 18 years if $2,000 is invested in accounts paying 5% interest compounded continuously. Answer (to the nearest dollar): $ P = r = t = in years as a decimal with a leading zero: 5% written as 0.05 no commas or $ Continuous Compounding A = Per•t Find the amount of money you will have after 30 years if $5,000 is invested in accounts paying 8% interest compounded continuously. Answer (to the nearest dollar): $ P = r = t = in years as a decimal with a leading zero: 5% written as 0.05 no commas or $ Continuous Compounding A = Per•t If you invest $10,000 for two years at an annual rate of 8%, compounded continuously, how much INTEREST will you make during the two years? remember, I only want the interest earned, not the total in the account. Answer (to the nearest dollar): $ P = r = t = in years as a decimal with a leading zero: 5% written as 0.05 no commas or $ Continuous Compounding A = Per•t If the world population is about 6 billion people now and if the population grows continuously at an annual rate of 1.7%, what will the population be in 10 years? Answer (to two decimals): P = r = t = billion in years as a decimal with a leading zero: 5% written as 0.05 Continuous Compounding billion A = Per•t Derek invested $1,500 into an account that pays 9% interest compounded continuously. How long must the money be left in the account for it to grow to $4,417? Answer (to the nearest whole year): P = r = t = ? ? ? ? in years as a decimal with a leading zero: 5% written as 0.05 no commas or $ Continuous Compounding A = Per•t |