STA 2191 FINANCIAL MATHEMATICS I CATI 12TH OCTOBER 2010 Instructions: Answer all questions 1. Express d)...

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STA 2191 FINANCIAL MATHEMATICS I CATI 12TH OCTOBER 2010 Instructions: Answer all questions 1. Express d) as a function of (3) 2. You deposit 1,000 today and another 2,000 in five years time into a fund that pays simple discount at 5% per year. Your friend makes the same deposits into another fund but at times n and 2n, respectively, the fund credits interest at an annual effective rate of interest of 10%. At the end of 10 years, the accumulated value of your deposits is exactly the same as the accumulated value of your friends deposits. Calculate n [3marks] 3. Calculate the time in days it takes for 3600 to accumulate to 4000 at: (i) A simple rate of interest of 6% p.a. (ii) A compound rate of interest of 6% p.a. convertible quarterly. (iii) A compound rate of interest of 6% p.a. convertible monthly. b. [5marks] 4. The force of interest 6(t) at time t is at +bt where a and b are constants. An amount of 1000 invested at time t= 0 accumulates to 1500 at time t = 5 and 2300 at time t= 10. Determine the value of a and [5marks] 5. The force of interest 8(t) is a function of time and at any time t (measured in years) is given by the formula 0.03+0.001 0 STA 2191 FINANCIAL MATHEMATICS I CATI 12TH OCTOBER 2010 Instructions: Answer all questions 1. Express d) as a function of (3) 2. You deposit 1,000 today and another 2,000 in five years time into a fund that pays simple discount at 5% per year. Your friend makes the same deposits into another fund but at times n and 2n, respectively, the fund credits interest at an annual effective rate of interest of 10%. At the end of 10 years, the accumulated value of your deposits is exactly the same as the accumulated value of your friends deposits. Calculate n [3marks] 3. Calculate the time in days it takes for 3600 to accumulate to 4000 at: (i) A simple rate of interest of 6% p.a. (ii) A compound rate of interest of 6% p.a. convertible quarterly. (iii) A compound rate of interest of 6% p.a. convertible monthly. b. [5marks] 4. The force of interest 6(t) at time t is at +bt where a and b are constants. An amount of 1000 invested at time t= 0 accumulates to 1500 at time t = 5 and 2300 at time t= 10. Determine the value of a and [5marks] 5. The force of interest 8(t) is a function of time and at any time t (measured in years) is given by the formula 0.03+0.001 0

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