Exam 4: Time Value of Money

Your Aunt Elsa has $500,000 invested at 6.5%,and she plans to retire.She wants to withdraw $40,000 at the beginning of each year,starting immediately.What is the maximum number of whole payments that can be withdrawn before the account is exhausted,i.e.,before the account balance would become negative? (Hint: Round down to the nearest whole number.)

Suppose you just won the state lottery,and you have a choice between receiving $2,550,000 today or a 20-year annuity of $250,000,with the first payment coming one year from today.What rate of return is built into the annuity? Disregard taxes.

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 bank pays 4% interest annually.You have $2,500 invested in the bank.How long will it take for your funds to double?

You borrowed $50,000 which you must repay in 10 years.You plan to make an initial deposit today,then make 9 more deposits at the beginning of each the next 9 years,but with the deposits increasing at the inflation rate.You expect to earn 5% on your funds,and you expect a 3% inflation rate.To the nearest dollar,how large must your initial deposit be to enable you to reach your $50,000 target?

What is the present value of the following cash flow stream at a rate of 8.0%?

Your older brother turned 35 today,and he is planning to save $7,000 per year for retirement,with the first deposit to be made one year from today.He will invest in a mutual fund that's expected to provide a return of 7.5% per year.He plans to retire 30 years from today,when he turns 65,and he expects to live for 25 years after retirement,to age 90.Under these assumptions,how much can he spend each year after he retires? His first withdrawal will be made at the end of his first retirement year.

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

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

All other things held constant,the present value of a given annual annuity decreases as the number of periods per year increases.

Suppose a Google.com bond will pay $4,500 ten years from now.If the going interest rate on safe 10-year bonds is 4.25%,how much is the bond worth today?

Your 75-year-old grandmother expects to live for another 15 years.She currently has $1,000,000 of savings,which is invested to earn a guaranteed 5% rate of return.If inflation averages 2% per year,how much can she withdraw (to the nearest dollar)at the beginning of each year and keep the withdrawals constant in real terms,i.e.,growing at the same rate as inflation and thus enabling her to maintain a constant standard of living?

You plan to borrow $35,000 at a 7.5% annual interest rate.The terms require you to amortize the loan with 7 equal end-of-year payments.How much interest would you be paying in Year 2?

You are considering two equally risky annuities,each of which pays $25,000 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?

If the discount (or interest)rate is positive,the present value of an expected series of payments will always exceed the future value of the same series.

A "growing annuity" is a cash flow stream that grows at a constant rate for a specified number of periods.

How much would Roderick have after 6 years if he has $500 now and leaves it invested at 5.5% with annual compounding?

You have $5,000 invested in a bank that pays 3.8% annually.How long will it take for your funds to triple?

If a bank compounds savings accounts quarterly,the nominal rate will exceed the effective annual rate.

Which of the following statements regarding a 20-year (240-month)$225,000,fixed-rate mortgage is CORRECT? (Ignore taxes and transactions costs.)