Tutorial03 - an annual effective rate of interest 4.5 Q6 A...

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Problem Set 3: ACTSC 231 Mathematics of Finance, Winter 2011 Q1. (a) Show algebraically that i + 1 s n e i = 1 a n e i . (b) Verbally explain why the equality in (a) must hold. Q2. (a) Show algebraically that d + 1 ¨ s n e i = 1 ¨a n e i . (b) Verbally explain why the equality in (a) must hold. Q3. A 5-year annuity-due pays $400 monthly payments in the first two years and then $300 monthly payments in the last three years. If annual nominal interest rate is 4.5% compounded monthly, what is the present value of this annuity? Q4. Kelly wishes to accumulate $250,000 in a college fund at the end of 18 years. If she deposits $10,000 in the fund at the beginning of each of the first nine years and $ X at the end of each of the second nine years, find X if the fund earns an annual effective rate of interest 5.5%. Q5. A family wishes to accumulate $90,000 in a college fund at the end of 18 years. If they deposit $1,000 in the fund at the end of each of the first 9 years and $(1 , 000 + X ) in the fund at the end of the second 9 years, find X to the nearest dollar if the fund earns
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Unformatted text preview: an annual effective rate of interest 4.5%. Q6. A loan of $30,000 is repaid by 32 monthly payments of $1,000 in arrears plus a final smaller payment. Using a interest rate of 6% compounded monthly determine the final payment. Q7. A debt of $20,000 will be paid off by the monthly payments of $1,000 at the end of each month at a nominal interest rate of 7.2% per year, compounded monthly. Find the number of level payments needed and the amount of the final smaller payment if it is made one month after the last level payment. Q8. Thierry plans to accumulate a fund for a retirement by depositing $3,000 at the be-ginning of each year for 25 years. Starting at the 26th year he can make 15 level withdrawals at the beginning of each year so as to deplete the fund. Assuming that all payments are level, find the amount of the annual withdrawal, if the effective rate of interest is 8% during the first 25 years but only 7% thereafter. 1...
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