jenis bs (Annuity duration) Find the duration D and the modified duration DM of a perpetual annuity that pays an amount A at the beginning of each year, with the first such payment being 1 year from now. Assume a constant interest rate r compounded yearly. [Hint: It is not necessary to evaluate any new summations.]

jenis bs (Annuity duration) Find the duration D and the modified duration DM of a perpetual annuity that pays an amount A at the beginning of each year, with the first such payment being 1 year from now. Assume a constant interest rate r compounded yearly. [Hint: It is not necessary to evaluate any new summations.]

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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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. What is the present value of a 3-year annuity of $110 if the discount rate is 5%? (Do not round intermediate calculations. Round your answer to 2 decimal places.) b. What is the present value of the annuity in (a) if you have to wait an additional year for the first payment? (Do not round intermediate calculations. Round your final answer to 2 decimal places.)
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For each of the following situations involving annuities, solve for the unknown. Assume that interest is compounded annually and that all annuity amounts are received at the end of each period. (i = interest rate, and n = number of years) (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided. Round your final answers to nearest whole dollar amount.) Present Value Annuity Amount i = n = 1. ? $2,400 8% 5 2. 533,082 140,000 ? 4 3. 583,150 180,000 9% ? 4. 530,000 75,502 ? 8 5. 235,000 ? 10% 4
For each of the following situations involving annuities, solve for the unknown. Assume that interest is compounded annually and that all annuity amounts are received at the end of each period. (i=interest rate, and n=number of years)(FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of 1$ and PVAD of $1) (Use appropriate factor (s) from the tables provided. Round your final answers to nearest whole dollar amount.) Present Value Annuity Amount i= n= ______________ $ 2,600 8% 5 507,866 135,000 _____ 4 661,241 170,000 9% ____ 540,000 78,557 _____ 8 230,000 _____________ 10% 4
Find the amount accumulated FV in the given annuity account. HINT [See Quick Example 1 and Example 1.] (Assume end-of-period deposits and compounding at the same intervals as deposits. Round your answer to the nearest cent.) $2,300 is deposited quarterly for 10 years at 7% per year FV = $
Task: Assume that at time 0 a sum L is lent for a series of n yearly payments. The rth payment, of amount x, is due at the end of the rth year. Let the effective annual interest rate for the rth year be i,. Give an identity which expresses L in terms of the x, and i,. Answer: The identity is [ Select ] [ Select ] L = x_1 (1+i_1)^(-1) + x_2 (1+i_1)^(-1) (1+i_2)^(-2) + .. + x_n (1+i_1)^(-1) (1+i_2)^(-2) ... (1+i_n)^(-n) L = x_1 (1+i_1) + x_2 (1+i_1) (1+i_2) + ... + x_n (1+i_1) (1+i_2) ... (1+i_n) L = x_1 (1+i_1)^(-1) + x_2 (1+i_1)^(-1) (1+i_2)^(-1) + .. + x_n (1+i_1)^(-1) (1+i_2)^(-1) ... (1+i_n)^(-1) Question 3 L = x_1 (1+i_1) + x_2 (1+i_1) (1+i_2)^2 + ... + x_n (1+i_1) (1+i_2)^2 ... (1+i_n)^n
What is the future value (at the end of 10 years) of an annuity that pays $700 a quarter over 10 years with the payments invested at 6.6% per annum (assume compounding matches payment periods, common assumption for such problems)? (enter your answer in the following format 123456.78) Answer:
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9. Examine the time line for Now the annuity shown. 250 (1.015) 250 (1.015) 250 (1.015) E 250 (1.015)23 250 (1.015) a) What is the duration of this annuity? How can you tell? b) Determine the annual rate of interest and the number of compounding periods per year. c) Determine the present value of this annuity. d) Determine the total interest earned. ANSWER 9. a) 6 years b) 6%; 4 compounding periods per year c) $5007.60 d) $992.40 Time (3-month periods) 1 2 250 250 250 250 250 3 23 24 H-H
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 more
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