Exam 4: Time Value of Money

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

Your aunt is about to retire,and she wants to buy an annuity that will supplement her income by $65,000 per year for 25 years,beginning a year from today.The going rate on such annuities is 6.25%.How much would it cost her to buy such an annuity today?

What's the present value of a perpetuity that pays $250 per year if the appropriate interest rate is 5%?

Which of the following statements is correct,assuming positive interest rates and other things held constant?

Your uncle has $300,000 invested at 7.5%,and he now wants to retire.He wants to withdraw $35,000 at the end of each year,beginning 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?

John and Daphne are saving for their daughter Ellen's university education.Ellen is now 10 years old and will be entering university 8 years from now (t = 8).University tuition and expenses at City U.are currently $14,500 a year,but they are expected to increase at a rate of 3.5% a year.John and Daphne expect Ellen to graduate in four years.(If Ellen 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 $15,000 in the university savings account.Their long-run financial plan is to add an additional $5,000 at the beginning of each of the next 4 years (at t = 0,1,2,and 3).Then they plan to make four equal annual contributions at the end of each of the following five years (t = 4,5,6,7,and 8).They expect their investment account to earn 9%.How large must the annual payments be at t = 4,5,6,7,and 8 to meet Ellen's anticipated university costs?

Suppose your credit card issuer states that it charges a 15.00% nominal annual rate.If you must make monthly payments,which amounts to monthly compounding,what is the effective annual rate?

Suppose you borrowed $12,000 at a rate of 9% and must repay it in 4 equal installments at the end of each of the next 4 years.How much would your payments be?

You are considering two equally risky annuities,each of which pays $5,000 per year for 10 years.Investment ORD is an ordinary (or deferred) annuity,while Investment DUE is an annuity due.Which of the following statements is correct?

You plan to make annual deposits into a bank account that pays a 5.00% nominal annual rate.You think inflation will amount to 2.50% per year.What is the expected annual real rate at which your money will grow?

When a loan is amortized,a relatively high percentage of the payment goes to reduce the outstanding principal in the early years,and the principal repayment's percentage declines in the loan's later years.

Disregarding risk,if money has time value,it is impossible for the present value of a given sum to exceed its future value.

You want to accumulate $2,500,000 in your RRSP by your retirement date,which is 35 years from now.You will make 30 deposits into your plan,with the first deposit occurring today.The plan's rate of return typically averages 9%.You expect to increase each deposit by 2% as your income grows with inflation.(That is,your second deposit will be 2% greater than your first,the third will be 2% greater than the second,etc.) How much must your first deposit at t = 0 be to enable you to meet your goal?

Your father now has $1,000,000 invested in an account that pays 9.00%.He expects inflation to average 3%,and he wants to make annual constant dollar (real) end-of-year withdrawals over each of the next 20 years and end up with a zero balance after the 20th year.How large will his initial withdrawal (and thus constant dollar [real] withdrawals) be?

An investment promises the following cash flow stream: $750 at Time 0; $2,450 at the end of Year 1 (or at t = 1); $3,175 at the end of Year 2; and $4,400 at the end of Year 3.At a discount rate of 8.0%,what is the present value of the cash flow stream?

Which of the following statements regarding the present value of an annuity is correct?

Which of the following bank accounts has the highest effective annual return?

How much would $5,000 due in 50 years be worth today if the discount rate were 7.5%?

Your sister wants to attend university.She is 13 years old and expects to begin university the year she turns 18.If university tuition is currently $10,000 annually,and inflation is 3%,what is the expected tuition cost of your sister's first year?

You deposit $1,000 today in a savings account that pays 3.5% interest,compounded annually.How much will your account be worth at the end of 25 years?