Exercise 5: (11 points)

1. What will be the accumulated value in 15 years of an annuity in progression geometry including the first annual payment of $700 and the 5th of $1033. Assume that:

• There are 15 installments to be made;
• The annual effective interest rate is 9%;
• The first payment will be made in one year and the last in 15 years.

2. Francine, who is currently 59 years old, plans to retire at the age of 65. At that time, she would like to receive an initial annual benefit of $25,000. Subsequently, on the date of each of her birthdays, she would wish, in order to preserve her purchasing power, to receive annual benefits indexed at the rate of 4% up to and including age 85.

Given an effective annual rate of return of 10%, how much does she need to invest now in order to receive the desired benefits?