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- Explain the term Present Value of Perpetuities?Suppose you deposited $200 at the end of every year for seven years in an account that earned 6% annual effevtive interest. At the end of seven years, how much would the account be worth?Show complete solution (please write eligibly) 1. Find the uniform annual amount that is equivalent to a uniform gradient series in which the first year’s payment is $500, the second year’s payment is $600, the third year’s payment is $700, and so on, and there are a total of 22 payments. The annual interest rate is 11%. Round answer to 2 decimal places. Use any of the following formula to solve the problem
- Two annuity dues in perpetuity have a common present value of $2, 000 and a common effective annual interest rate i. The first annuity makes payments of $100 at the beginning of every three years and the second makes payments of X at the beginning of every three months. Find X.5 Question Let Ya,n be the present value of an n-year term continuous annuity of $1 per year for an insured aged x. Let Y be the present value of a whole life continuous annuity of $1 per year for an insured aged x. Given a constant force of interest, 8, show that: 1 бп Cov (Yz,n, Yz) = (A — e¯ðª‚„Ez (1 − Āz+n) — ±‚ñ¦Ã‚) 82 n. - -6) Two annuities in perpetuity have the same effective annual interest rate. The first annuity pays $40 every 5 years, starting at the end of the 10th year and has present value $100. The second annuity pays $20 at the end of each 3 months, starting at the beginning of the first three months. Find the present value of the second annuity.
- 4. At an annual effective interest rate of i, i > 0, both of the following annuities have a present value of Y: (a) a 10-year annuity-immediate with annual payments of 55. (b) a 15-year annuity-immediate with annual payments that pays 30 per year for the first 5 years, per year for the second 5 years, and 90 per year for the final 5 years. 60 Calculate Y. Solution:A state lottery gives a winner the choice of receiving the winning amount in equal monthly payments for 20 years or receiving a lump sum equal to the present value of an annuity with future value equal to the winnings. The winner selecting monthly payments will receive $4,000,000/240 = $16,666.67 each month for each million dollars of winnings. (Round your final answers to two decimal places.) (a) Find the present value of an annuity with monthly payments of $16,666.67, at an Interest rate of 5.2% for 20 years, for the winner who wants a lump-sum payment. $ X (b) In order for the lottery to be more profitable, it is decided to pay the winnings in equal monthly payments for 25 years. Find the monthly payments of $4 million in winnings. $ Find the present value of an annuity with those monthly payments at 5.2% for 25 years. $Fact 21 Eileen has 2.5% of her earnings deposited into her retirement plan. If $150 per month is deposited in the plan, find ner monthly and yearly earnings. 8. Her monthly earnings are $ (Round to the nearest cent as needed.) Her yearly earnings are $ (Round to the nearest cent as needed.) 09 C.SU7 365 https://xlitemprod.pearsoncmg.com/api/v1/print/math
- Please answer using Annuity Formula. Step by step. Thank you.Find an expression for the present value of an annuity on which payments are 1 at the end of each 4-month period for 12 years assuming a rate of interest per 3-month period.A rich relative has bequeathed you a growing perpetuity. The first payment will occur in a year and will be $3,000. Each year after that, you will receive a payment on the anniversary of the last payment that is 4% larger than the last payment. This pattern of payments will go on forever. Assume that the interest rate is 15% per year. a. What is today's value of the bequest? b. What is the value of the bequest immediately after the first payment is made? ARCKICHI a. What is today's value of the bequest? Today's value of the bequest is $(Round to the nearest dollar. b. What is the value of the bequest immediately after the first payment is made? The value of the bequest immediately after the first payment is made is $ (Round to the nearest dollar.)