Tutorial05

# Tutorial05 - values to the nearest 0.0001(a 200 a(4 10 e...

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Problem Set 5: ACTSC 231 Mathematics of Finance, Winter 2011 Q1. Find the present value of a ten-year annuity which pays \$500 at the end of each month for the ﬁrst 4 years and \$2,000 at the end of each quarter for the last 6 years. Annual eﬀective interest rate is 7%. Q2. A family puts \$2,000 every two years in a fund that earns a 5% annual rate. On the day of the 10th payment, they transfer the accumulated amount into a fund that pays X at the beginning of each month for four years, and that earns 4% annual eﬀective rate. Determine X . Q3. A perpetuity paying \$1,000 at the beginning of each two years has the same present value as another perpetuity with level payments, this one having payments at the end of each three years. Express the level payment amount of the second annuity as a function of the annual eﬀective interest rate i . Q4. Carefully describe what each of the following symbols measures and calculate their
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Unformatted text preview: values to the nearest 0.0001: (a) 200 a (4) 10 e 6% ; (b) 1200¨ s (12) 20 e 4% . Q5. Compare these four symbols ¨ a n e i , ¨a ( m ) n e i , a ( m ) n e i and a n e i by calculating their values at n = 48, m = 12 and i = 5%. Q6. If ¯ a n e = 6 . 321206 and ¯ s n e = 17 . 182818, then ﬁnd δ and n . Q7. Anita receives a 20-year annuity which make monthly payments in arrear. The monthly payments in the ﬁrst year are all \$500 and the payments increase by \$10 each year. Find the present value of this annuity, if the annual interest rate is 12% convertible monthly. Q8. Beatrice takes out a \$20,000 loan for ten years at an annual interest rate of 6% con-vertible quarterly. The loan is repaid by quarterly payments which start at \$ P as the ﬁrst payment and then grow by 10% quarterly. Find P . 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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