Perpetuity A provides payments of 3000 every six months with the first payment six months from today. Perpetuity B provides payments of the amount of k every two years with the first payment due now. An annual effective interest rate of 4.94% is given. The two perpetuities have the same present value. Determine the value of the payment k.
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Perpetuity A provides payments of 3000 every six months with the first payment six months from today.
Perpetuity B provides payments of the amount of k every two years with the first payment due now.
An annual effective interest rate of 4.94% is given. The two perpetuities have the same
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- If Bergen Air Systems takes out a $100,000 loan, with eight equal principal payments due over the next eight years, how much will be accounted for as a current portion of a noncurrent note payable each year?Annuity A pays 1 at the beginning of each year for five years.Annuity B pays 1 at the beginning of each year for four years.The Macaulay duration of Annuity A at the time of purchase is Σ/10. Both annuities offer thesame yield rate.Calculate the Macaulay duration of Annuity B at the time of purchase. Σ=22A 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 more
- Consider 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%.)The following two annuities-immediate are available for purchase: (a) the first annuity makes annual payments of 1000 for twenty years, (b) the second annuity is a perpetuity that also has annual payments. The payment in each of the first ten years is 600. Beginning in year 11, the payments increase to 1200, and remain at 1200 forever. At an annual effective interest rate of i > 0, both annuities have a present value of X. Calculate XAn annuity due which pays 100 per month for 12 years has a present value of 7,908. Calculate the annual effective interest rate used to determine the present I value.
- Find the payment that should be used for the annuity due whose future value is given. Assume that the compounding period is the same as the payment period. $168, 000; monthly payments for 5 years; interest rate 3% .A 20-year annuity X has annual payments of $10,000 at the beginning of each year for 10 years, then annual payments of $20,000 at the beginning of each year for the next 10 years. A perpetuity Y has payments of Q at the end of each year for 10 years, then payments of 2Q at the end of each year thereafter. The present values of X and Y are equal when calculated using an annual effective interest rate of 5%. Find Q.The present values of the following three annuities are equal: • perpetuity immediate paying 1 year year, calculated at an annual effective interest rate of 7.25%. • 50-year annuity immediate paying 1 each year, calculated at an annual effective interest rate of j%. • n−year annuity immediate paying 1 each year, calculated at an annual effective interest rate of j − 1%. Calculate n.
- There is a perpetuity due in which the payments increase by 5 percent per year, and the present value of the 6’th payment is equal to the present value of the 8’th payment. The first payment is 500 dollars. Find both the effective interest rate and the present value.What is the present value of a perpetuity consisting of equal payments of $66 every 3 months, where the first payment occurs 3 months from now, and the interest rate is 12% p.a.?The compounding periods and the payment periods are the same for an annuity and for an amortization. Determine the present value of the annuity that will pay the given periodic payments. (Round your final answer to two decimal places.) Monthly payments of $430 for 5 years with a monthly interest rate of 0.8%.