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.

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.

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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Annuity payments are assumed to come at the end of each payment period (termed an ordinary annuity). However, an exception occurs when the annuity payments come at the beginning of each period (termed an annuity due). What is the future value of a 15-year annuity of $1,600 per period where payments come at the beginning of each period? The interest rate is 9 percent. Use Appendix C for an approximate answer, but calculate your final answer using the formula and financial calculator methods. To find the future value of an annuity due when using the Appendix tables, add 1 to n and subtract 1 from the tabular value. For example, to find the future value of a $100 payment
At an annual effective interest rate of 5%, an annuity immediate with 4N level annual payments of 1000 has a present value of 14,898.13. Determine the fraction of the total present value represented by the first set of N payments and the third set of N payments combined. A. 0.579 B. 0.585 C. 0.614 D. 0.643 E. 0.672
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.
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.) Periodic payments of $2400 annually for 13 years. The interest is 4% compounded annually.
What is thevpresent value of an annuity of 1,600 per year for 10 years, with the first payment occurring at the end of year 10 ( that is, ten 1,600 payments occurring at the end of year 10 through year 19), given a discount rate of 9 percent?
14. Annuity A pays X at the end of each year. The first payment occurs at time 6 years, and the last payment occurs at time 10 years. Annuity B pays $81.06 at the end of each year. The first payment occurs at time 1 year, and the last payment occurs at time 5 years. The current value of annuity B at the end of five years is $475.54. The present value at time 0 of annuity A is twice the present value at time 0 of annuity B. Determine X. D 350 E 387 A 238 C 313 B 275
Find the following values assuming a regular, or ordinary, annuity: a. The present value of $400 per year for ten years at 10 percent. b. The future value of $400 per year for ten years at 10 percent. c. The present value of $200 per year for five years at 5 percent.d. The future value of $200 per year for five years at 5 percent.Repeat Problem above but assume the annuities are annuities due.(Dollar signs, decimal places, and commas all matter)
You will receive 100 annual perpetuity starting at year 0, a 300 annual perpetuity with the first payment at the end of year 5, and a 200 semiannual perpetuity with the first payment in the middle of year 10. If you require an effective annual interest rate of 14.49 percent, what is the future value of all three perpetuities together.
What is the present value of a 8-year ordinary annuity with annual payments of $511, evaluated at a 4 percent interest rate? Round your answer to 2 decimal places; for example 2345.25.
You are comparing two annuities with equal present values. The applicable discount rate is 7.25%. One annuity pays $2,500 on the first day of each year for 15 years. How much does the second annuity pay each year for 15 years if it pays at the end of each year?
A 13-year annuity pays $1,200 per month, and payments are made at the end of each month. The interest rate is 13 percent compounded monthly for the first five years and 11 percent compounded monthly thereafter. What is the present value of the annuity?

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