1. A 20-year annuity immediate pays 2000 for the first year. In each subsequent year, cach payment is increased by $300 over the payment from the previous year. The nominal annual interest rate is 18% convertible monthly. Calculate the present valuc of this annuity.
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- You want to invest $8,000 at an annual Interest rate of 8% that compounds annually for 12 years. Which table will help you determine the value of your account at the end of 12 years? A. future value of one dollar ($1) B. present value of one dollar ($1) C. future value of an ordinary annuity D. present value of an ordinary annuityAnnuity A has 20 years annual payments as follows:- i) ii) iii) Annuity i) ii) iii) The first payment is 1000 made at the end of the first year. The subsequent payments increase by 3% from the previous years. The effective interest rate is 5% per annum. B has 20 years annual payments as follows:- The first payment is X made at the end of the first year. The subsequent payments increase by X from the previous years. The effective interest rate is 6% per annum. Annuity C is an annuity immediate of 20-year annual level payments with effective interest rate of 7% per annum. Evaluate, (a) Present value of Annuity A (b) X if present value of Annuity A is equal to present value of Annuity B. stelua. [3 marks] (c) Level payment of Annuity C if present value of Annuity C is TWICE the present value of Annuity A. (d) Sum of future value of these annuities at the end of 20 years. 13 marks] Preval 13 marksConsider two perpetuities (X and Y) at interest rate i. X provides level payments of $105 at the end of each year. Y provides a payment of $5 at the end of the first year, with payments increasing by $5 annually. Find i such that the present value of (X-Y) is a maximum. (Answer to the nearest .05%.)
- Suppose an annuity pays $2000 at the end of each 3 month period for 3.5 years at an interest rate of 4%, compounded quarterly a. find the total number of periods b. find the real interest rate per period c. find the present value (give the formula)A one-year annuity that pays $100 semi-annually will starts its payment in 6 months from now. APR is 8 percent compounded semi-annually. a. What is the present value of the annuity? b. What is the effective annual rate? c. Now consider another one-year annuity that makes a “single” payment in a year from now. How much should it pay to the investor if it is equally valuable to the previous annuity?Suppose an annuity at 5% compounded semi-annually will pay $5000 at the end of each 6-month period for 7 years with the first payment deferred for 13 years.(a) What is the number of payment periods and the number of deferral periods?(b) What is the interest rate per period?(c) Find the present value of this annuity.
- Annuity X pays $1,200 at each year-end for 15 years. Annuity Y pays $1,100 at the beginning of each year for 15 years. The effective annual rate is 8%. Which one is correct? Annuity X has a higher present value than Annuity Y. Annuity Y has a higher present value than Annuity X. Annuity X has the same present value as Annuity Y.a. Calculate the annual cash flows ( annuity payments) from a fixed- payment annuity if the present value of the 20-year annuity is $1.4 million and the annuity earns a guaranteed annual return of 10 percent. The payments are to begin at the end of the current year. b. Calculate the annual cash flows (annuity payments) from a fixed - payment annuity if the present value of the 20-year annuity is $1.4 million and the annuity earns a guaranteed annual return of 10 percent. The payments are to begin at the end of six years.A 10-year annuity-due with quarterly payments has a first payment of 1000. The next five payments are also 1000, and then subsequent payments increase by 5.06% over their previous payment. Determine the present value of the annuity using an interest rate of 8%, compounded quarterly. A) 58,295 B) 59,570 C) 60,845 D) 62,120 E) 63,395
- The present value of a 5-year annuity is X. The annuity pays 600 at the end of the first month, 590 at the end of the second month, and for each month thereafter the payment decreases by 10. The annual nominal interest rate is 3% compounded monthly. Calculate X. A 16,402.37 B 16,834.05 C 16,845.29 D 17,390.57 E 17,402.37The present value of a 10-year annuity immediate is 10,000$. The interest rate is j1=5% for the first 5years, j1=6% for 2 following years and j1=7% for the continuing years. Find the value of one payment (R)A 5-year annuity has a series of payments 1, 2, 3, 2, 1 with the first payment made at time t = 0 and each subsequent payment occurring one year later than the previous. The present value (i.e. value at time 0) of this annuity is 8.41 using an effective annual interest rate of i. A 6-year annuity has a series of payments 1, 2, 3, 3, 2, 1 with the first payment made at time t = 0 and each subsequent payment occurring one year later than the previous. Find the present value (i.e. value at time 0) of the 6-year annuity at the interest rate i.