Reference no: EM133043039

Questions - Annuity at Maturity and Commencement

1. To purchase a car of the year, 24 payments of $10,500 must be made each month, starting at the time the car is delivered (beginning of the period). The agency charges an annual interest rate of 30% capitalizable each month. You are asked to determine the price if the payments are made at the beginning of the term.

2. A group of friends decide to open a savings account at a bank to deposit each week for 28 weeks, in order to do some activity for everyone in the summer. The amount is $6000 per week. There are two options:

a) Bancomer offers them a rate of 19.22% per annum compoundable each week if the deposits are made at the beginning of the week.

b) Banamex offers them a rate of 3.5% compoundable each week if they make the deposits at the beginning of the period.

c) Determine the best option and why.

3. Santiago deposited $5,000 at the end of each quarter for 3 years. If he did not make any withdrawals in all this time and his bank paid him 1% compoundable interest every quarter, how much did he collect at the end of the 3 years? What if the deposits were made at the beginning of the year?

4. Mrs. Castruita, mother of 10-year-old Laurita, has started saving so that her daughter can go to college. She plans to deposit $2,000 in a savings account at the end of each month for the next 18 years. If the nominal interest rate is 9% per year, how much will she have collected at the end of 8 years?

5. A company purchased a machine for $12,000 on credit to be paid off in 5 annual payments at an interest rate of 14% per annum. After the second payment, the terms of the sale were changed to allow the account to be settled in one payment. What is the final amount?

6. It is your desire to build your own retirement fund so that 15 years from now you can have an annual income of $144,000 for 20 years. If we assume that the average investment rate for the next 15 years is 8%, how much do you need to deposit today?

7. Assume that Don Jaime wishes to retire 30 years from today. Doing a little analysis, he determines that he can live on $50,000 per year. The first withdrawal will occur one year after his retirement. Don Jaime estimates that the interest rate at the bank is 6% per year and he wishes to receive the funds for 25 more years. What amount will allow Don Jaime to meet his retirement plan? If the withdrawals are made at the beginning of the period, how much does the amount change for the retirement plan?