Question 1. Suppose that you invest P dollars at the beginning of every week. However, your crazy banker decides to compound interest at a rate r at the end of Week 5, Week 9, Week 12, Week 14, and Week 15.

1. What is the value of the account at the end of Week 15?

2. At the end of the Week 15, you need to spend $15, 000 on a bandersnatch. How much money must you invest

weekly to ensure you have exactly $15, 000 after Week 15 if the weekly interest rate is 10%?

Question 2. Your crazy banker presents another investment opportunity for 2022, where you are told that for the first six months of the year you will have an APR of r1 compounded monthly, and for the second half of the year the APR will be r2 compounded monthly. Assume that interest compounds on the 28th day of each month.

1. The banker tells you that for the first six months of the year the effective annual rate is a1 = 6%, but they refuse to divulge the value of r1 directly. You choose to invest $1000 on January 1, 2022, and decide to withdraw all funds from the account on June 30, 2022. What was the value of your account upon withdrawal?

2. The banker then informs you that for the last six months of the year the effective continuous rate is c2 = 4%. You decide that it would be nice to have exactly $2000 in this account on December 15, 2022. What amount of money do you need to invest in this account on July 1, 2022, in order to accomplish this goal?