Paola purchases a 10 year annuity immediate with an annual effective rate of interest of 7.0718% and annual payments of 10x. Kurt purchases a 10 year decreasing annuity immediate with annual payments and an effective rate of interest of 7.0718%. His first payment is $50 and subsequent payments are reduced by an amount equal to X. Both annuities have the same present value. Calculate X.
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Paola purchases a 10 year
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- Janet receives a $ 10,000 life insurance benefit. If she uses the proceeds to buy an n-year annuity immediate, the annual payout will be 1534.86. If a 2n-year annuity due is purchased, the annual payout will be 994.13. Both calculations are based on an effective annual interest rate of i. Calculate i.Delia purchases an annuity that will pay her $10,000 per year for the next 10 years starting next year. Assuming a rate of 6%, what is the value of the annuity. Choose the closest. a) $106,000 b) $131,808 c) $159,374 d) $171,569Christina will receive a 5-year annuity of $1,200 a year, with the first payment occurring at Date 4. What is the value of this annuity to her today at a discount rate of 7.25 percent? A. $4,111.08 B. $4,209.19 C. $4.774.04 D. $3,961.80 E. $4,887.48 The answer given is E, however, mine is D. Could you help me to explain this question?
- A perpetuity of $1 each year, with the first payment due immediately, has a present value of $25 at an annual effective rate of i%. The owner exchanges it for another perpetuity with the first payment due immediately and subsequent payments due at two year intervals. What should the payment of the second perpetuity be, in order to keep the same interest rate, i%, and the same present value? A B с D E Less than $1.90 At least $1.90, but less than $1.94 At least $1.94, but less than $1.98 At least $1.98, but less than $2.02 $2.02 or moreJane receives payments of X at the beginning of each year forever. The present value of her annuity is 460.May receives payments of 6X at the beginning of each year for 2n years. The present value of her annuity is 2600. If both accounts have the same annual effective rate of interest, i, calculate vn. Round your answer to 4 decimal places.Amy purchases an annuity that will give her payments of R at the end of each quarter for seven years. She will receive the first of these payments in 1.5 years. If Amy paid $50,000 for this annuity and will earn a nominal rate of interest of 6% compounded quarterly,(a) write the equation of value (using the appropriate actuarial notation) for this annuity at the time of purchase. Be sure to indicate the effective rate per payment period being used.(b) find the value of R.
- 9. Implied interest rate and period Consider the case of the following annuities, and the need to compute either their expected rate of return or duration. A. Anthony inherited an annuity worth $3,811.62 from his uncle. The annuity will pay him four equal payments of $1,100 at the end of each year. The annuity fund is offering a return of . B. Anthony’s friend, Jack, wants to go to business school. While his father will share some of the expenses, Jack still needs to put in the rest on his own. But Jack has no money saved for it yet. According to his calculations, it will cost him $32,406 to complete the business program, including tuition, cost of living, and other expenses. He has decided to deposit $4,200 at the end of every year in a mutual fund, from which he expects to earn a fixed 10% rate of return. It will take approximately for Jack to save enough money to go to business school.(1)Strahd bought a 20-year annuity-immediate with payment size 350 at an annual effective rate of 4%. Just after receiving the eighth payment, Strahd’s life forever changed and he sold the remainder of the annuity, reinvesting the proceeds in a level-payment perpetuityimmediate. What is the payment size K of this perpetuity?Shawn purchases a retirement annuity that will pay him $1,000 at the end of every six months for the first nine years and $300 at the end of every month for the next six years. The annuity earns interest at a rate of 2.8% compounded quarterly. a. What was the purchase price of the annuity? Round to the nearest cent b. How much interest did Shawn receive from the annuity? Round to the nearest cent
- Trish receives $450 on the first of each month. Josh receives $450 on the last day of each month. BothTrish and Josh will receive payments for next four years. At a discount rate of 9.5 percent, what is thedifference in the present value of these two sets of payments?Select one:a. $151.06b. $141.80c. $162.50d. $159.08e. $154.30Michelle purchases a retirement annuity that will pay her $3,000 at the end of every six months for the first eleven years and $600 at the end of every month for the next five years. The annuity earns interest at a rate of 2.3% compounded quarterly. a. What was the purchase price of the annuity? Round to the nearest cent b. How much interest did Michelle receive from the annuity? Round to the nearest centJoe can purchase one of two annuities: Annuity 1: A 10-year decreasing annuity-immediate, with annual payments of 10, 9, 8, 1. Annuity 2: A perpetuity-immediate with annual payments. The perpetuity pays 1 in year 1, 2 in year 2, 3 in year 3., and 11 in year 11. After year 11, the payments remain constant at 11. At an annual effective interest rate of i, the present value of Annuity 2 is twice the present value of Annuity 1. Calculate the value of Annuity 1. A 8 с D 36.4 37.4 38.4 394