Quiz 2 Math 618 Name 1. Kathryn deposits 100 into an account at the beginning of each 4-year period for 40 years. The account credits interest at an annual effective interest rate of i. The accumulated amount in the account at the end of 40 years is X, which is 5 times the accumulated amount in the account at the end of 20 years. Calculate X. A. 4695 B. 5070 C. 5445 D. 5820 E. 6195 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. A. 17 B. 18 C. 19 D. 20 E. 21 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 At the end of each year, the interest earned plus an additional 100 is withdrawn from the fund.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. A. 1519 B. 1819 C. 2085 D. 2273 E. 2431 4. A perpetuity-immediate pays 100 per year. Immediately after the fifth payment, the perpetuity 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. A. 54 B. 64 C. 74 D. 84 E. 94 5. 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. For year 6 and all future years, the current year?s payment is K% larger than the previous year?s payment. At an annual effective interest rate of 9.2%, the perpetuity has a present value of 167.50. Calculate K, given K < 9.2. A. 4.0 B. 4.2 C. 4.4 D. 4.6 E. 4.8 6. To accumulate 8000 at the end of 3n years, deposits of 98 are made at the end of each of the first n years and 196 at the end of each of the next 2n years. The annual effective rate of interest is i. You are given (1 +i)n = 2. Determine i. A. 11.25% B. 11.75% C. 12.25% D. 12.75% E. 13.25% 7. Olga buys a 5-year increasing annuity for X. Olga will receive 2 at the end of the first month, 4 at the end of the second month, and for each month thereafter the payment increases by 2. The nominal interest rate is 9% convertible quarterly. Calculate X. A. 2680 B. 2730 C. 2780 D. 2830 E. 2880 8. A perpetuity-immediate pays X per year. Brian receives the first n payments, Colleen receives the next n payments, and Jeff receives the remaining payments. Brian?s share of the present value of the original perpetuity is 40%, and Jeff?s share is K. Calculate K. A. 24% B. 28% C. 32% D. 36% E. 40% 9. At an annual effective interest rate of i > 0, the present value of a perpetuity paying 10 at the end of each 3-year period, with the first payment at the end of year 3, is 32. At the same annual effective rate of i, the present value of a perpetuity paying 1 at the end of each 4-month period, with first payment at the end of 4 months, is X. Calculate X. A. 31.6 B. 32.6 C. 33.6 D. 34.6 E. 35.6 10. An insurance company has an obligation to pay the medical costs for a claimant. Average annual claims costs today are $5,000, and medical inflation is expected to be 7% per year. The claimant is expected to live an additional 20 years. Claim payments are made at yearly intervals, with the first claim payment to be made one year from today. Find the present value of the obligation if the annual interest rate is 5%. A. 87,932 B. 102,514 C. 114,611 D. 122,634 E. Cannot be done 11. A man turns 40 today and wishes to provide supplemental retirement income of 3000 at the beginning of each month starting on his 65th birthday. Starting today, he makes monthly contributions of X to a fund for 25 years. The fund earns a nominal rate of 8% compounded monthly. On his 65th birthday, each 1000 of the fund will provide 9.65 of income at the beginning of each month starting immediately and continuing as long as he survives. Calculate X. A. 324.73 B. 326.89 C. 328.12 D. 355.45 E. 450.65
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