given the choice of investing 1000 00 at an annual rate of 6

given the choice of investing $1000 00 at an annual rate of 6%, compounded either and observe the slight difference in each curve. Then use a table to compare the graphs numerically Let Y represent the investment compounded annually, and let Y2 represent the investment compounded monthly. Graph both Y is the difference between the retums on each investment after 1 year, 2 years, 5 years, 10 years, 20 years, 30 years, and 40 What ine the difference in returns of the two investments 40 rs the final answers to two decimal places as needed. Round all intermediate values to six decimal places as needed.) as

Solution

money invested = $ 1000

rate = 6%

compounded annually after 1 year = 1000 ( 1 + .06 )^1 = 1060

monthly after 1 year = 1061.68

difference = $ 1.68

annually after 2 years = 1000 ( 1 + .06)^2 = 1123.60

monthly after 2 years = 1127.16

difference = $ 3.56

annually after 5 years = 1000 ( 1 + .06) ^5 = 1338.23

monthly after 5 years = 1348.85

difference = $ 10.62

annually after 10 years = 1790.85

monthly after 10 years = 1819.40

difference = $ 28.55

annually after 20 years = 3207.14

monthly after 20 years = 3310.20

difference = $ 103.06

annually after 30 years = 5743.49

monthly after 30 years = 6022.58

difference = $ 279.09

annually after 40 years = 10285.72

monthly after 40 years = 10957.45

difference = $ 671.73