1. Ken recently got a raise. He decided to save all the extra money in a special...

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1. Ken recently got a raise. He decided to save all the extra money in a special account. His raise amounts to $150 every 2 weeks (26 times per year). The account earns 5.2% annually compounded every 2 weeks. He opened the account at the time of the first deposit so each deposit is made at the start of the two week period. It has been 11 weeks and Ken is thinking about his balance. Below is a table he has made to analyze his account balance after the first 5 deposits. Complete the table.

March 19 ^th Analysis of Account
Deposit Number	Deposit Date	Number of Compounding Periods	Contribution of Deposit to Current Balance
1	January 1
2	January 15
3	January 29
4	February 12
5	February 26
6	March 12

2. Jen started saving $1,000 every quarter 5 years ago in an account earning 4% compounded quarterly. She has just made her 20 ^th deposit. There was only one quarter when she could not make her savings goal. The second quarter of this, her fifth, year she had some unexpected expenses and was not able to make what would have been her 18 ^th deposit. Her Mom surprised her with money so the annuity continued. Jen’s current balance is $22,019. How much of that is due to her Mom’s gift? [Of course it is more than the $1,000 her Mom gave her.] Justify your answer mathematically.

3. Consider an ordinary annuity with deposits made monthly beginning in June 2009 and continuing for 4 years. Below is the future value of the annuity (at some point during the term of the annuity).

250(1.0075) ⁵ + 250(1.0075) ⁴ + 250(1.0075) ³ + 250(1.0075) ² + 250(1.0075) + 250

3a. For this account, what are the regular deposit amount, the periodic interest rate, the nominal rate, and the number of deposits made so far?

3b. What is the full range of calendar dates that the expression above represents the future value of the account?

4. Pauline graduated and got a great job. She started saving regularly the first week of January and was able to deposit $50 each week into an account earning 5.2% interest compounded weekly. She did this for a full year before getting a raise and increasing her deposits. Below is the future value of the annuity (at some point during the year).

50 + 50(1.001) + 50(1.001) ² + … + 50(1.001) ⁹ + 50(1.001) ¹⁰

When was the deposit corresponding to the term 50(1.001) ² made? Do not give the calendar date. Rather give the number of the week of the deposit (as in week 1, week 2, and so on).