ACTSC 231 Tutorial07

# ACTSC 231 Tutorial07 - P as the ﬁrst payment and then...

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Problem Set 7: ACTSC 231 Mathematics of Finance, Fall 2010 Q1. Payments are made into an account continuously at a rate of 8 Y + tY per year, for 0 t 10. At time T = 10, the account is worth \$20, 000. Find Y if the account earns interest according to a force of interest δ t = 1 / (8 + t ) at time t , for 0 t 10. Q2. A 2-year deferred annuity paying continuously at a rate of 300 + 200 t per year, for 2 t 10. Find the present value of this annuity, if the force of interest function δ t = 5 / (3 + 2 t ) for 0 t 10. Q3. If ¯ a n e = 6 . 321206 and ¯ s n e = 17 . 182818, then ﬁnd δ and n . Q4. 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. Q5. 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 \$
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Unformatted text preview: P as the ﬁrst payment and then grow by 10% quarterly. Find P . Q6. A 30-year bond has 9% annual coupons and a face value of \$1,000. It is redeemed at par. Coupons are reinvested at nominal rate of 6% convertible semi-annually. Find the bond price P such that the overall yield for the investor is 10% eﬀective per year. Q7. A \$1,000 bond with a coupon rate of 9% per year payable semiannually is redeemed at \$1,125 after an unspeciﬁed number of years. The yield of this bond is 10% convertible semiannually. If the present value of the redemption value is \$225 at this yield rate, ﬁnd the bond price. Q8. A \$1,000 bond with a coupon rate of 6% per year payable semiannually is redeemed at par on July 1, 2017. Its purchase price on July 1, 2009 is 1015.85. Find its book value on January 1, 2012. 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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