STA 2190: INTRODUCTION TO ACTUARIAL SCIENCE CAT II 27TH NOVEMBER 2012 INSTRUCTIONS: Answer all questions 1....

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STA 2190: INTRODUCTION TO ACTUARIAL SCIENCE CAT II 27TH NOVEMBER 2012 INSTRUCTIONS: Answer all questions 1. An amount X is deposited in an account that earns interest at an annual effective rate of interest 7%. Another amount is deposited in another account that earns interest at an annual effective rate of discount d. After 8 years, the total interest earned by both accounts is equal. Find d [6 marks] 2. Suppose you lend KSh.4,820 to your sister on Sept 14, at an annual rate of simple interest of 10%, to be repaid on Dec 25. How much does she have to pay you back? [2 marks] 3. What is the effective rate of interest corresponding to an interest rate of 5% compounded quarterly [2 marks] 4. Bruce and Robbie each open up new bank accounts at time 0. Bruce deposits 1000 into his bank account, and Robbie deposits 500 into his. Each account earns an annual effective interest rate of i. The amount of interest earned in Bruce's account during the 11th year is equal to X. The amount of interest earned in Robbie's account during the 17th year is also equal to X. Calculate X. [4 marks] 5. Denote by dm) the rate of discount payable m times per year. What is the relationship between dm) and i and between d(m) and (m). [2 marks] 6. A certain company issues both debenture stocks and unsecured loan stocks. Describe the differences between these two types of assets. [4 marks] 7. List the main issuers of bonds [4 marks] 8. Summarize the features of treasury bills and government bonds. [6 marks] STA 2190: INTRODUCTION TO ACTUARIAL SCIENCE CAT II 27TH NOVEMBER 2012 INSTRUCTIONS: Answer all questions 1. An amount X is deposited in an account that earns interest at an annual effective rate of interest 7%. Another amount is deposited in another account that earns interest at an annual effective rate of discount d. After 8 years, the total interest earned by both accounts is equal. Find d [6 marks] 2. Suppose you lend KSh.4,820 to your sister on Sept 14, at an annual rate of simple interest of 10%, to be repaid on Dec 25. How much does she have to pay you back? [2 marks] 3. What is the effective rate of interest corresponding to an interest rate of 5% compounded quarterly [2 marks] 4. Bruce and Robbie each open up new bank accounts at time 0. Bruce deposits 1000 into his bank account, and Robbie deposits 500 into his. Each account earns an annual effective interest rate of i. The amount of interest earned in Bruce's account during the 11th year is equal to X. The amount of interest earned in Robbie's account during the 17th year is also equal to X. Calculate X. [4 marks] 5. Denote by dm) the rate of discount payable m times per year. What is the relationship between dm) and i and between d(m) and (m). [2 marks] 6. A certain company issues both debenture stocks and unsecured loan stocks. Describe the differences between these two types of assets. [4 marks] 7. List the main issuers of bonds [4 marks] 8. Summarize the features of treasury bills and government bonds. [6 marks]

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