ACTSC 231 Tutorial01

ACTSC 231 Tutorial01 - while Grandparents B will fund the...

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Problem Set 1: ACTSC 231 Mathematics of Finance, Fall 2010 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. \$600 invested for two years will provide interest of \$264 in total. Then, with the same rate of compound interest per year, what will be the amount of interest earned from a \$2,000 investment for three years? Q4. 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? Q5. Let A K (4) = 1000 and i n = 0 . 01 n for all positive integers n . Find ﬁnd A K (7). Q6. A fund needs to be created so that a newborn will have \$25,000 per year for four years starting at age 18. Grandparents A decide to fund the two ﬁrst \$25,000 payments,
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Unformatted text preview: while Grandparents B will fund the third and fourth payment. What is the dierence between the investment required (at time 0) by grandparents A and B, if they both invest at an annual eective rate of 4%? Q7. A bank pays an annual eective rate i on investments. You are told that \$500 invested today will accumulate to \$566 after ve years. Find the (combined) present value of three payments of \$5,000 at time 10, 15 and 20. Q8. Robin deposits \$4,300 into an account on March 1, 1998. The bank guarantees that the annual eective rate for the balance under \$5,000 is 3.5% and for the balance over \$5,000 is 5%. Suppose that there is no other deposits or withdrawals except for one withdrawal of \$ 1,000 on March 1, 2003 and a deposit of \$500 on March 1, 2004. Find his account balance on March 1, 2006. 1...
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