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2. Two people, Ella and Jane, decide to start saving for retirement. Ella decides to invest \$4000 a year into an annuity at the age of 25. At the age of 35 she stops making investments and just leaves the money there. Jane on the other hand, decides to start investing \$4000 a year at the age of 40 and invests that money for every year thereafter. Assuming both retire at 70, and that the interest rate both get on their investments is 10% (compounded annually) who has the most money in their account at age 70? Explain why you pick the answer you pick.

Question 3

(10 points)

3. At the age of 30 you decide to start saving money. At first you can only afford to deposit \$200 per month. However, at the age of 38 you are able to deposit \$300 per month. Then at the age of 45 you raise your monthly deposit again to \$500 per month. Finally at the age of 50 you get promoted to president of the company and are able to deposit \$2000 per month into the account. Assuming your account is earning (prime interest rate + 4%) in interest, compounded monthly, how much do you have in your account at the age of 70? Hint: Treat each time that you change the deposit amount as a seperate annuity, and compute the future value (FV) on each annuity seperately. Assume that each annuity earns compound interest during the time it is not receiving deposits.

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