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# Tutorial01 - (a) Compound interest at eﬀective annual...

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Problem Set 1: ACTSC 231 Mathematics of Finance, Winter 2011 Q1. Given that A K ( t ) = t 3 + 2 t 2 + 4 t + 16, ﬁnd a ( t ) and i 3 . Q2. At a particular annual rate of simple interest, \$1,200 invested at time 0 will accumulate to \$1,320 in T years. Find the accumulated value of \$100 invested at t = 0 at the same rate of simple interest, but for T/ 2 years. Q3. Tom deposits \$900 in a savings account. The annual eﬀective rate is 2% for the ﬁrst two years. For the next three years it is 3%, and for the following ﬁve years it is 4%. What is Tom’s balance at the end of ten years? Q4. Let A K (4) = 1000 and i n = 0 . 01 n for all positive integers n . Find ﬁnd A K (7). Q5. A bank pays an annual eﬀective rate i on investments. You are told that \$500 invested today will accumulate to \$566 after ﬁve years. Find the (combined) present value of three payments of \$5,000 at time 10, 15 and 20. Q6. A loan of face amount X , due in one-half year, is valued \$4,992 today. Find X under each of the following interest calculation methods.
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Unformatted text preview: (a) Compound interest at eﬀective annual rate 8% (b) Simple interest at annual rate 8% (c) Compound discount at eﬀective annual rate 8% (d) Simple discount at annual rate 8% Q7. Bank A pays interest at rate i (2) = 15%. Bank B pays interest compounded daily. What minimum nominal annual rate must Bank B pay in order to be as attractive as Bank A? Assume we have 365 days in one year. Q8. Consider a 4-year investment with an annual simple discount rate of 10%. Find the equivalent annual simple interest rate i over the same investment period. Q9. Suppose we have compound interest and an eﬀective monthly interest rate of 0.5%. Find equivalent rates i (12) , i , and d . Q10. If the eﬀective annual rate of discount is 8%, for how long do you need to invest a principal of \$500 so that it will accumulate to \$750? 1...
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## This note was uploaded on 07/13/2011 for the course ACTSC 231 taught by Professor Chisholm during the Winter '09 term at Waterloo.

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