(a) Describe Sues savings profile and compare it to Joes. Why does Sue end up with a substantially larger retirement nest egg than does Joe, even though she saves a lot less?

(b) If Sue stopped saving at age 40, the age Joe starts saving, how much less would she have when she retires at age 65? What if she stopped saving at age 30? What if she continued saving all the way to age 65? (Change the spreadsheet to obtain the answers.)

(c) Go back to the original spreadsheet and change the interest rate to different values, both smaller and larger than the given 8%. Consider at least 5 different interest rates. Report what you find. How do different interest rates affect total accumulation of savings for Joe and Sue. Make small table summarizing the results.

2. Suppose you expect a stock to pay a dividend of $10 every year forever and the discount rate is fixed at 5%.

(a) What would expect the price of that stock is priced according to its present value?

(b) What happens to the price of the stock if the discount rate falls to 2%?

(c) Now suppose you expect the dividend to grow by 1.5% every year, such that it will be $10.15 next year, $10.30 the year after that, and so on. What are the new prices of the stock with 5% and 2% discount rates?

(Note: this exercise might help explain why the stock market and home prices are so high these days, despite the COVID-19 pandemic and lackluster economy.

Sue saves $5000 per year starting at age 20, saving a total of 230,000 by age 65 Joe waits until age 40, and then saves $10000 per year, saving a total of $260,000 by age 65 With an interest rate of 8%, how big are their nest eggs at age 65? Age 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 Interest rate: 0.08 Sue Joe Contribution Interest Balance Age Contribution Interest Balance 5000 200 5,200 20 5000 616 10,816 21 5000 1,065.28 16,881.28 22 5000 1,550.502 23,431.782 23 5000 2,074.543 30,506.325 24 5000 2,640.506 38,146.831 25 5000 3,251.746 46,398.577 26 5000 3,911.886 55,310.464 27 5000 4,624.837 64,935.301 28 5000 5,394.824 75,330.125 29 5000 6,226.41 86,556.535 30 5000 7,124.523 98,681.058 31 5000 8,094.485 111,775.542 32 5000 9,142.043 125,917.586 33 5000 10,273.407 141,190.992 34 5000 11,495.279 157,686.272 35 5000 12,814.902 175,501.174 36 5000 14,240.094 194,741.267 37 5000 15,779.301 215,520.569 38 5000 17,441.646 237,962.214 39 5000 19,236.977 262,199.191 40 10000 400 10,400 5000 21,175.935 288,375.127 41 10000 1,232 21,632 5000 23,270.01 316,645.137 42 10000 2,130.56 33,762.56 5000 25,531.611 347,176.748 43 10000 3,101.005 46,863.565 5000 27,974.14 380,150.888 44 10000 4,149.085 61,012.65 5000 30,612.071 415,762.959 45 10000 5,281.012 76,293.662 5000 33,461.037 454,223.995 46 10000 6,503.493 92,797.155 5000 36,537.92 495,761.915 47 10000 7,823.772 110,620.927 5000 39,860.953 540,622.868 48 10000 9,249.674 129,870.602 5000 43,449.829 589,072.698 49 10000 10,789.648 150,660.25 5000 47,325.816 641,398.514 50 10000 12,452.82 173,113.07 5000 51,511.881 697,910.395 51 10000 14,249.046 197,362.115 5000 56,032.832 758,943.226 52 10000 16,188.969 223,551.084 5000 60,915.458 824,858.684 53 10000 18,284.087 251,835.171 5000 66,188.695 896,047.379 54 10000 20,546.814 282,381.985 5000 71,883.79 972,931.169 55 10000 22,990.559 315,372.544 5000 78,034.494 1,055,965.66 56 10000 25,629.803 351,002.347 5000 84,677.253 1,145,642.91 57 10000 28,480.188 389,482.535 5000 91,851.433 1,242,494.34 58 10000 31,558.603 431,041.138 5000 99,599.548 1,347,093.89 59 10000 34,883.291 475,924.429 5000 107,967.512 1,460,061.40 60 10000 38,473.954 524,398.383 5000 117,004.913 1,582,066.32 61 10000 42,351.871 576,750.254 5000 126,765.306 1,713,831.62 62 10000 46,540.02 633,290.274 5000 137,306.53 1,856,138.15 63 10000 51,063.222 694,353.496 5000 148,691.053 2,009,829.21 10000 55,948.28 760,301.776 5000 160,986.337 2,175,815.54 65 10000 61,224.142 831,525.918 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 64 65 Total Saved: 230,000 260,000 Sue saves $5000 per year starting at age 20, saving a total of 230,000 by age 65 Joe waits until age 40, and then saves $10000 per year, saving a total of $260,000 by age 65 With an interest rate of 8%, how big are their nest eggs at age 65? Age 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 Interest rate: 0.08 Sue Joe Contribution Interest Balance Age Contribution Interest Balance 5000 200 5,200 20 5000 616 10,816 21 5000 1,065.28 16,881.28 22 5000 1,550.502 23,431.782 23 5000 2,074.543 30,506.325 24 5000 2,640.506 38,146.831 25 5000 3,251.746 46,398.577 26 5000 3,911.886 55,310.464 27 5000 4,624.837 64,935.301 28 5000 5,394.824 75,330.125 29 5000 6,226.41 86,556.535 30 5000 7,124.523 98,681.058 31 5000 8,094.485 111,775.542 32 5000 9,142.043 125,917.586 33 5000 10,273.407 141,190.992 34 5000 11,495.279 157,686.272 35 5000 12,814.902 175,501.174 36 5000 14,240.094 194,741.267 37 5000 15,779.301 215,520.569 38 5000 17,441.646 237,962.214 39 5000 19,236.977 262,199.191 40 10000 400 10,400 5000 21,175.935 288,375.127 41 10000 1,232 21,632 5000 23,270.01 316,645.137 42 10000 2,130.56 33,762.56 5000 25,531.611 347,176.748 43 10000 3,101.005 46,863.565 5000 27,974.14 380,150.888 44 10000 4,149.085 61,012.65 5000 30,612.071 415,762.959 45 10000 5,281.012 76,293.662 5000 33,461.037 454,223.995 46 10000 6,503.493 92,797.155 5000 36,537.92 495,761.915 47 10000 7,823.772 110,620.927 5000 39,860.953 540,622.868 48 10000 9,249.674 129,870.602 5000 43,449.829 589,072.698 49 10000 10,789.648 150,660.25 5000 47,325.816 641,398.514 50 10000 12,452.82 173,113.07 5000 51,511.881 697,910.395 51 10000 14,249.046 197,362.115 5000 56,032.832 758,943.226 52 10000 16,188.969 223,551.084 5000 60,915.458 824,858.684 53 10000 18,284.087 251,835.171 5000 66,188.695 896,047.379 54 10000 20,546.814 282,381.985 5000 71,883.79 972,931.169 55 10000 22,990.559 315,372.544 5000 78,034.494 1,055,965.66 56 10000 25,629.803 351,002.347 5000 84,677.253 1,145,642.91 57 10000 28,480.188 389,482.535 5000 91,851.433 1,242,494.34 58 10000 31,558.603 431,041.138 5000 99,599.548 1,347,093.89 59 10000 34,883.291 475,924.429 5000 107,967.512 1,460,061.40 60 10000 38,473.954 524,398.383 5000 117,004.913 1,582,066.32 61 10000 42,351.871 576,750.254 5000 126,765.306 1,713,831.62 62 10000 46,540.02 633,290.274 5000 137,306.53 1,856,138.15 63 10000 51,063.222 694,353.496 5000 148,691.053 2,009,829.21 10000 55,948.28 760,301.776 5000 160,986.337 2,175,815.54 65 10000 61,224.142 831,525.918 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 64 65 Total Saved: 230,000 260,000