8. Roger and Samantha are brother and sister that will split an inheritance equally. Roger spends his share on a perpetuity due paying 60,000 for the first 20 years and 90,000 thereafter. The price of this perpetuity is based on an annual effective rate of 4%. Samantha spends her share on an n year deferred perpetuity due paying 308,961.6427 annually, and the price she pays for her perpetuity is based on an annual effective rate of 5%. Find n.

8. Roger and Samantha are brother and sister that will split an inheritance equally. Roger spends his share on a perpetuity due paying 60,000 for the first 20 years and 90,000 thereafter. The price of this perpetuity is based on an annual effective rate of 4%. Samantha spends her share on an n year deferred perpetuity due paying 308,961.6427 annually, and the price she pays for her perpetuity is based on an annual effective rate of 5%. Find n.

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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John's estate is to be divided into three equal parts and invested, to be paid out as follows: i. John's two children will each receive their share in 20 level annual payments, beginning one year after John's death. ii. Charity Q will receive its share as equal annual payments in perpetuity beginning 21 years after John's death. Q's annual payment is twice the annual payment for one child. Determine the effective interest rate at which the estate is invested. Less than 5% At least 5% but less than 5.25% At least 5.25% but less than 5.5o% At least 5-50% but less than 5.75% At least 5.75%
On Sarah’s 18th birthday, she creates a trust fund to pay her a sequence of nine semiannual payments of 15,000; the first is due on her 23rd birthday. If the fund earns 6.5% compounded semiannually, find the present value of the deferred annuity.
Nancy, who is 59 years old, is the beneficiary of a $235,000 life insurance policy. What amount of the insurance proceeds is taxable under each of the following scenarios? Note: Do not round any intermediate division. Round your final answer to the nearest whole dollar amount. a. She receives the $235,000 proceeds as a lump-sum payment. b. She receives the proceeds at the rate of $4,525 a month for five years. c. She receives the proceeds in monthly payments of $1,370 over her remaining life expectancy (assume she will live 25 years). d. Use the information from (c). If Nancy lives beyond her 25-year life expectancy, what amount of each monthly payment will be taxable in the 26th year? a. Taxable insurance proceeds b. Taxable insurance proceeds per month c. Taxable insurance proceeds per month d. Taxable insurance proceeds per month $
Juanita paid a life insurer $60,100 in exchange for an immediate life annuity. Juanita will receive $600 per month from the insurer, and her life expectancy is 14 years. Assume that Juanita receives 12 monthly payments in the first year. How much taxable income must she report? (Round your answer to 2 decimal places)
Joseph Kirn has just inherited $827,790 which he would like to use as part of his retirement nest egg. He invested the funds at a 3.47 percent annual rate compounded annually. Joseph will reach age sixty in 17 years and will retire early. Now he would like to know how much he could withdraw from the fund in equal installments at the end of each year from the year he reaches age 60 until he reaches age 70½, the year he must start withdrawing funds from his individual retirement account (IRA). Joseph assumes the funds will continue to earn at a 3.47 percent annual rate. In other words, Joseph would like to know the annual year-end payment from an eleven-year annuity (from age 60 to the year he will be 70½), earning 3.47 percent annually. Round the answer to two decimal places.
Carl is the beneficiary of a $ 20,000 trust fund set up for him by his grandparents. Under the terms of the trust, he is to receive the money over a 5-year period in equal installments at the end of each year. If the fund earns interest at the rate of 5%/year compounded annually, what amount will he receive each year? (Round your answer to the nearest cent.) $
Geoff purchased a life annuity for $4,800 that will provide him $100 monthly payments for as long as he lives. Based on IRS tables, Geoff’s life expectancy is 240 months. How much of the first $100 payment will Geoff include in his gross income?
Daniel purchases a perpetuity with varying annual payments made in arrears. During the first 5 years, the payments are constant and equal to 10 per year. Beginning in year 6, the payments start to increase. For year 6 and all subsequent years, the payment in that year is p% larger than the payment in the year immediately preceding that year, where p < 9.2. At an annual effective interest rate of 9.2%, the perpetuity has a present value of 167.50. Calculate p, to 2 decimal places.
Two brothers, Mark and Charles, each inherit $30000$⁢30000. Mark invests his inheritance in a savings account with an annual return of 3.1%3.1%, while Charles invests his inheritance in a CD paying 5.8%5.8%annually. How much more money than Mark does Charles have after 11year?
Matt is age 75. He received $4,000 from an annuity in 2021. He paid $40,000 for that annuity in 2010. The annuity will pay Matt $4,000 a year, for 15 years, starting in 2011. How much of the $4,000 is included in Matt’s taxable income in 2021? ( ) $0 ( ) $4,000 ( ) $2,668 ( ) $1,332
3. Billy and Mandy Eastwood recently divorced, and Mandy has custody of their 5-year-old daughter. As part of the divorce settlement, Billy must pay Mandy $3,000 at the end of each half year until their daughter reaches age 16. Billy decides to put a lump sum into an account with a guaranteed yield of 5% compounded semiannually. Find the lump sum deposit he must make today to equal the balance of the annuity after 13 years.

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