Exercise 4: Points a and b are independent

1. What will be the accumulated value in 14 years of a geometric progression annuity with the first annual payment of $650 and the fifth of $1,100? Suppose that:

• There are 15 installments to be made;
• The first payment will be made in exactly one year and the last in 14 years;
• The annual effective interest rate is 10%.

1. Find the present value of a $1000 perpetuity payable at the beginning of each semester if the semi-annual capitalized nominal rate is 10%.

Exercise 5:

1. An individual invests $300 in an RRSP at the end of each month for 5 years. How much money will he have at the end of this period if the nominal rate of return capitalized monthly is 8%?

1. An investor is able to invest their money at an annual rate of 10% and wants to receive $15,000 at the beginning of each year for 5 years. Determine how much they need to invest now.

1. On a property put up for sale, Mr. Dupont offered $19,000 payable in cash, Mrs. Durand

$27,000 due in 8 years and Mr. Francis $23,000 payable in 6 years. What is the best offer if the quarterly capitalized nominal rate is 8%?

Exercise 6:

1. Francine, who is currently 58 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 5% up to and including the age of 80.

Given an effective annual rate of return of 12%, how much should she invest now in order to receive the desired benefits?

1. A 35-year-old investor wants $900,000 when he or she turns 65. How much does he need to invest now at a nominal rate of 14% capitalized semi-annually to accumulate this sum?