By the end of each month Peggy puts 200 into a personal pension fund. After 35 years she wants to get a monthly payment for an indefinite time. The payment should be by the end of the month as well.

a) (2 Points) What is the monthly rate she is paid each month if the interest rate of her pension fund is 5.3% and after the 35 years the interest rate drops to 3.71%.

b) (1 Point) Which one-time investment would she have to make today to realize the same result? (Assume an interest rate of 5.3%.)

c) (2 Points) Assume that after 15 years she increases her savings to 500 per month. How much does the monthly rate she is paid after 35 years change from the result in a)?

d) (3 Points) Assuming Peggy saves as indicated in part a). After 35 years she starts taking money out of the account. By the beginning of each month she takes out 600 while the interest rate lies at 3.71%. For how long will the saved money suffice?

e) (2 Points) Provide a table illustrating the payout plan in part d)