Review_Exam2 - ACF329 Practice Problems for Exam 2 Warning...

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ACF329 Practice Problems for Exam 2 Warning: this is not a sample test. It is merely a supplement for your preparation. Name: Instructions: You should use one of the SOA approved calculators on this worksheet. These problems are from the sample Exam FM problems you can access from the Society of Actu- aries webpages. Some of them are slightly modified. Make sure you know how to use your calculator. I will not answer any questions during the exam on how to use the calculator. For example, “BGN” versus “END”; although it’s possible to calculate all annuity symbols with just one of them, it may be more convenient to be able to use both. 1. John borrows 10,000 for 10 years at an annual effective interest rate of 10%. He can repay this loan using the amortization method with payments of 1,627.45 at the end of each year. Instead, John repays the 10,000 using a sinking fund that pays an annual effective interest rate of 14%. The deposits to the sinking fund are equal to 1,627.45 minus the interest on the loan and are made at the end of each year for 10 years. Determine the balance in the sinking fund immediately after repayment of the loan. 2. A perpetuity costs 77.1 and makes annual payments at the end of the year. The perpetuity pays 1 at the end of year 2, 2 at the end of year 3, . . . , n at the end of year ( n + 1). After year ( n + 1), the payments remain constant at n . The annual effective interest rate is 10.5%. Calculate n . 3. 1000 is deposited into Fund X, which earns an annual effective rate of 6%. At the end of each year, the interest earned plus an additional 100 is withdrawn from the fund. At the end of the tenth year, the fund is depleted. The annual withdrawals of interest and principal are deposited into Fund Y, which earns an annual effective rate of 9%. Determine the accumulated value of Fund Y at the end of year 10. 4. A 20-year loan of 1000 is repaid with payments at the end of each year. Each of the first ten payments equals 150% of the amount of interest due. Each of the last ten payments is X . ACF329 Spring 2011 Harper
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The lender charges interest at an annual effective rate of 10%. Calculate X . 5. A perpetuity-immediate pays 100 per year. Immediately after the fifth payment, the perpe- tuity is exchanged for a 25-year annuity immediate that will pay X at the end of the first year. Each subsequent annual payment will be 8% greater than the preceding payment. The annual effective rate of interest is 8%. Calculate X . 6. Mike buys a perpetuity-immediate with varying annual payments. During the first 5 years, the payment is constant and equal to 10. Beginning in year 6, the payments start to increase.
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