Exam 5: Time Value of Money

Your uncle has $340,000 invested at 7.5%,and he now wants to retire.He wants to withdraw $35,000 at the end of each year,starting at the end of this year.He also wants to have $25,000 left to give you when he ceases to withdraw funds from the account.For how many years can he make the $35,000 withdrawals and still have $25,000 left in the end?

Which of the following statements is CORRECT?

Which of the following statements is CORRECT?

After graduation,you plan to work for Dynamo Corporation for 12 years and then start your own business.You expect to save and deposit $7,500 a year for the first 6 years (t = 1 through t = 6)and $15,000 annually for the following 6 years (t = 7 through t = 12).The first deposit will be made a year from today.In addition,your grandfather just gave you a $32,500 graduation gift which you will deposit immediately (t = 0).If the account earns 9% compounded annually,how much will you have when you start your business 12 years from now?

Midway through the life of an amortized loan,the percentage of the payment that represents interest must be equal to the percentage that represents repayment of principal.This is true regardless of the original life of the loan or the interest rate on the loan.

Your uncle is about to retire,and he wants to buy an annuity that will provide him with $57,000 of income a year for 20 years,with the first payment coming immediately.The going rate on such annuities is 5.25%.How much would it cost him to buy the annuity today?

Which of the following statements is CORRECT?

Your grandmother just died and left you $47,500 in a trust fund that pays 6.5% interest.You must spend the money on your college education,and you must withdraw the money in 4 equal installments,beginning immediately.How much could you withdraw today and at the beginning of each of the next 3 years and end up with zero in the account?

You have a chance to buy an annuity that pays $1,400 at the beginning of each year for 3 years.You could earn 5.5% on your money in other investments with equal risk.What is the most you should pay for the annuity?

You have a chance to buy an annuity that pays $16,000 at the beginning of each year for 5 years.You could earn 4.5% on your money in other investments with equal risk.What is the most you should pay for the annuity?

A time line is meaningful even if all cash flows do not occur annually.

Suppose you borrowed $75,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each of the next 5 years.By how much would you reduce the amount you owe in the first year?

Pace Co.borrowed $30,000 at a rate of 7.25%,simple interest,with interest paid at the end of each month.The bank uses a 360-day year.How much interest would Pace have to pay in a 30-day month?

You want to buy a new ski boat 2 years from now,and you plan to save $7,000 per year,beginning one year from today.You will deposit your savings in an account that pays 6.2% interest.How much will you have just after you make the 2nd deposit,2 years from now?

Your sister turned 35 today,and she is planning to save $85,000 per year for retirement,with the first deposit to be made one year from today.She will invest in a mutual fund that's expected to provide a return of 7.5% per year.She plans to retire 30 years from today,when she turns 65,and she expects to live for 25 years after retirement,to age 90.Under these assumptions,how much can she spend each year after she retires? Her first withdrawal will be made at the end of her first retirement year.

What is the present value of the following cash flow stream at a rate of 10.0%? ​

Your child's orthodontist offers you two alternative payment plans.The first plan requires a $3,500 immediate up-front payment.The second plan requires you to make monthly payments of $137.41,payable at the end of each month for 3 years.What nominal annual interest rate is built into the monthly payment plan?

Suppose a State of New York bond will pay $1,000 ten years from now.If the going interest rate on these 10-year bonds is 4.9%,how much is the bond worth today?

John and Daphne are saving for their daughter Ellen's college education.Ellen just turned 10 (at t = 0),and she will be entering college 8 years from now (at t = 8).College tuition and expenses at State U.are currently $14,500 a year,but they are expected to increase at a rate of 3.5% a year.Ellen should graduate in 4 years--if she takes longer or wants to go to graduate school,she will be on her own.Tuition and other costs will be due at the beginning of each school year (at t = 8,9,10,and 11). So far,John and Daphne have accumulated $18,000 in their college savings account (at t = 0).Their long-run financial plan is to add an additional $5,000 in each of the next 4 years (at t = 1,2,3,and 4).Then they plan to make 3 equal annual contributions in each of the following years,t = 5,6,and 7.They expect their investment account to earn 9%.How large must the annual payments at t = 5,6,and 7 be to cover Ellen's anticipated college costs?

What is the present value of the following cash flow stream at a rate of 7.00%? ​