Exercise 1: These exercises (1-1-1 to 1-1-5) are independent of each other

1. Let's say you've just turned 20. Your wealthy grandparents set up a trust fund for you so that you would receive $140,000 by age 35. If the discount rate is 8%, what is the value of the fund today?

1. We offer you an investment of 10% per year. If you invest $15,000, how long will it take to get $30,000?

1. In 1867, Mr. George Edward Lee found an astrolabe (a 17th century navigational tool) that Samuel de Champlain had lost on his land in Ontario. Mr. Lee sold the astrolabe to a stranger for $12. In 1989, the Canadian Museum of Civilization purchased the astrolabe for $250,000 from its then-owner, the New York Historical Society (where it had ended up after many adventures). Obviously, Mr. Lee had been scammed. Imagine, however, that he had invested his $10 to 10%. How much would this sum be worth in 2021?.

1. You put $6000 in a bank. The annual continuous capitalization interest rate is 10%. What will be the value of this deposit after 5 years? .

1. What is the present value of $2,000 to be received in 4 years if the nominal rate with continuous capitalization is 8%? .

Exercise 2: Points 1.1 and 1.2 are independent

2. Nominal rate of 24% capitalized semi-annually;
3. Nominal rate of 24% capitalized monthly;
4. Nominal rate of 24% capitalized quarterly;
5. Annual effective rate of 25%;
6. Nominal rate of 23% capitalized monthly;
7. Nominal rate of 22.5% on a continuous capitalization basis.

1. Which of the following rates is best for the borrower?
2. Which of the following rates is best for the lender?

You deposit $950 at a financial institution at the beginning of each quarter for 30 quarters. How much money would you have in 10 years if the semi-annual capitalized nominal interest rate offered is 10%?

Exercise 3: Points a and b are independent

1. You invest $20,000 at a nominal rate of 8% capitalized semi-annually for a period of 10 years. Determine the total amount of interest earned between the beginning of year 5 and the end of year 9. (3 points)

1. What will be the accumulated value in 10 years of the next installment series?

• $1,500 to be paid at the end of Year 2;
• $1,000 to be paid in 3 years and 7 months;
• $3,500 to be paid in 8 years and 4 months;

The annual effective interest rate is 10%.