1. Your objective is an annuity due paying $5,000 semi-annually for 5 years at 4% compounded quarterly. How far in advance of this would you need to invest $20,000 at 6.82% compounded monthly? Assume 30 days in a month.

2. Jeff and Sarah want an ordinary annuity to pay their daughter $1,000 monthly for three years and nine months for the duration of her educational studies starting August 1, 2024. What lump-sum amount do they need to invest on August 1, 2014, if the deferred annuity can earn 6.6% compounded monthly during the accumulation stage and 4% compounded quarterly during the income payments stage?

3. Yarianny wants to withdraw $25,000 annually starting today for the next 20 years and will increase the withdrawals by 3.5% each year. If the annuity can earn 6% compounded semi-annually, how much money needs to be invested in the fund today?

4. Nikolay wants to make annual contributions to his RRSP for the next 25 years. He will increase each annual payment by 4.5%, and the RRSP can earn 9.3% compounded annually. If he wants to accumulate $250,000, what is the amount of his first payment today?

5. If $2,500,000 was invested at 4.8% compounded semi-annually, what payment at the end of every six months could be sustained in perpetuity?

6. Samson just won the grand prize of $50 million in the Lotto Max lottery. If he invests the money into a perpetuity fund earning 5.5% compounded annually, what monthly payment can he expect to receive starting today?

7. Quarterly payments are to be made against a $47,500 loan at 5.95% compounded annually with a six-year amortization. 25 marks (5 for each part) a. What is the size of the quarterly payment? b. Calculate the principal portion of the sixth payment. c. Calculate the interest portion of the 17th payment. d. Calculate how much the principal will be reduced in the fourth year. e. Calculate the total interest paid in the first year.

8. A $28,250 loan at 9% compounded quarterly is repaid by monthly payments over five years. a. What is the amount of the final payment? b. Calculate the principal and interest portions of the payments in the final year. 15 marks (7.5 for each)