Dave and Doug were twins. They both went to work at age 22 with identical jobs, and at the end of each year they received identical bonuses of $2,000. However, the twins invested their money differently.

Dave: Dave believed that as a young man he should take the opportunities to enjoy life and not be too concerned about saving for the future - he had many years to put money into savings. For the first 12 years he spent his $2000 bonuses on vacations. At age 34, he decided he should start saving for his future and from that time on, he invested his $2000 bonus each year into a savings program paying 3.5% compounded annually. This continued for 30 years (not counting the first year when the first $2000 was deposited).

1. What is this type of investment called?

compounded annually

2. What does it mean to compound annually?

3. Even though this is not the ideal way to track such an investment, we will demonstrate the process of depositing and compounding annually using a table. Finish the table which shows year number, starting amount, interest earned, total after interest added, total after $2000 added. Assume the $2000 deposit was done at the end of each year. Manually calculate interest, using I = Prt, for each year. (You could also use a spreadsheet to assist you with the calculations!)

Age/Year of Investment	Starting Amount	Interest Earned	Total after Interest Added	Total after $2000 Added
34 / 1	2000	0	2000+0=2000	$2000
35 / 2	$2000	$70	$2000 + 70 = $2070	$2070 + 2000 = $4070
36 / 3	$4070	$142.45	4070+142.45=4212.45	4212.45+2000=6212.45
37 / 4	6212.45	217.43	6212.45+217.43=6429.88	6429.88+2000=8429.88
38 / 5	8429.88	295.04	8429.88+295.04=8724.92	8724.92+2000=10724.92
39 / 6	10724.92	375.37	10724.92+375.37=11100.29	11100.29+2000=13100.29
40 / 7	13100.29	458.51	13100.29+458.51-13558.8	13558.8+2000=15558.8

This would be interesting to continue, but there is a much easier way to calculate Daves total amount of savings when he is ready to retire at age 64 years.

4. How much money will Dave have in his account when he is 64 years old? Use the correct formula to compute this, and use 30 years in the formula (since interest is calculated and added for 30 years). Show inputs to the formula below, as well as your answer.

Doug: As a young man, beginning at age 22, Doug was conservative and was concerned about his future. Each year he invested his $2000 bonuses in a savings program earning 3% interest compounded monthly. After 16 years, at age 38, Doug decided to have some fun in life and he began spending his $2000 bonuses on vacations instead of saving them. This continued until the end of his 64th year. Meanwhile, his savings continued to grow, compounded monthly at 3%.

1. Write in words the types of calculations needing to be done to solve this problem. (Hint: There are two steps.)

2. What does it mean to compound monthly?

3. Using the correct formulas, show the two steps needed to calculate the value of the account at the end of Dougs 64th year.

It is important to realize that for the first 16 years, if Dougs money was compounded monthly, he was also investing monthly. Therefore, for the annuity, assume that 1/12 of $2000 (rounded to the nearest cent) was the regular payment being invested each month.

Compare:

Compare the total savings for each of the twins going into retirement at the end of their 64th year of life. List each, and then describe why you think the results occur the way they do. Dont worry about trying to find the perfect answer, as your reasoning is much more important here!

Also, do you think that either of the twins has enough money to retire?