ACTSC 231 Tutorial03

# ACTSC 231 Tutorial03 - the year 2009 are as follows: There...

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Problem Set 3: ACTSC 231 Mathematics of Finance, Fall 2010 Q1. Suppose money accumulates at a varying force of interest given by δ t = 0 . 05 + 0 . 01 t for 0 t 4. Find the present value of two payments of 100 each to be paid at times t = 2 and t = 4. Q2. Find d 5 if (i) the rate of simple interest is 10%; (ii) the rate of simple discount is 10%; (iii) the force of interest is constant δ = 0 . 1. Q3. If the force of the interest for the coming year will be δ and the force of interest of inﬂation will be γ , show that the inﬂation-adjusted force of interest is δ - γ . Q4. Jennifer deposits \$1,000 into a bank account. The bank credits interest at nominal annual rate of i convertible semi-annually for the ﬁrst 7 years and a nominal annual rate of 2 i convertible quarterly for all years thereafter. The accumulated amount in the account at the end of 5 years is \$ X . The accumulated amount in the account at the end of 10.5 years is \$1,980. Calculate X . Q5. The fund value is reported after every transaction and at year end. The details during
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Unformatted text preview: the year 2009 are as follows: There are two deposits made: \$200 on 02/28/09 and Date ((MM/DD/YY)) Fund values 01/01/09 1,000 03/01/09 1,240 09/01/09 1,600 11/01/09 1,080 01/01/10 900 \$200 on 08/31/09. Also, there are two withdrawals made: \$500 on 10/31/09 and \$200 12/31/09. Then, nd the time-weighted annual yield rate (or annual rate of return). Q6. For the previous question, nd (a) the exact dollar-weighted rate of return (b) the approximate DWRR based on (i) simple-interest approximation; (ii) basic midpoint rule. Q7. Amy borrows \$10,000 from Ale at time 0. She pays back 2000 after 1 months, 3000 after 6 months and 5500 after 10 months. Find the annual interest rate on the loan. Q8. In the previous question, assume Ale can reinvest the payments received by Amy at a 10% rate convertible monthly. Then what is Ales return on this investment? 1...
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## This note was uploaded on 01/21/2011 for the course ACTSC 231 taught by Professor Chisholm during the Fall '09 term at Waterloo.

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