Exam 4: Time value of money

Your aunt has $500, 000 invested at 5.5%, and she now wants to retire.She wants to withdraw $45, 000 at the beginning of each year, beginning immediately.When she makes her last withdrawal (at the beginning of a year), she also wants to have enough left in the account so that you can make a final withdrawal of $50, 000 at the end of that year (her last withdrawal is at the beginning of the year, your withdrawal is at the end of that same year).What is the maximum number of $45, 000 withdrawals that she can make and still have enough in the account so that you can make a $50, 000 withdrawal at the end of the year of her last withdrawal? (Hint: If your solution for N is not an integer, round down to the nearest whole number.)

Now that your uncle has decided to retire, he wants to buy an annuity that will provide him with $85, 000 of income a year for 25 years, with the first payment coming immediately.The going rate on such annuities is 5.15%.How much would it cost him to buy the annuity today?

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

A perpetuity pays $85 per year and costs $950.What is the rate of return?

What is the present value of the following cash flow stream at a rate of 12.0%?

Your bank account pays an 8% nominal rate of interest.The interest is compounded quarterly.Which of the following statements is CORRECT?

If we are given a periodic interest rate, say a monthly rate, we can find the nominal annual rate by dividing the periodic rate by the number of periods per year.

Assume that you own an annuity that will pay you $15, 000 per year for 12 years, with the first payment being made today.You need money today to open a new restaurant, and your uncle offers to give you $120, 000 for the annuity.If you sell it, what rate of return would your uncle earn on his investment?

What is the present value of the following cash flow stream at a rate of 6.25%?

Your bank offers to lend you $100, 000 at an 8.5% annual interest rate to start your new business.The terms require you to amortize the loan with 10 equal end-of-year payments.How much interest would you be paying in Year 2?

The greater the number of compounding periods within a year, then (1)the greater the future value of a lump sum investment at Time 0 and (2)the greater the present value of a given lump sum to be received at some future date.

You have purchased a U.S.Treasury bond for $3, 000.No payments will be made until the bond matures 10 years from now, at which time it will be redeemed for $5, 000.What interest rate will you earn on this bond?

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.What is the maximum number of $35, 000 withdrawals that he can make and still have at least $25, 000 left in the account? (Hint: If your solution for N is not an integer, round down to the nearest whole number.)

If we are given a periodic interest rate, say a monthly rate, we can find the nominal annual rate by multiplying the periodic rate by the number of periods per year.

What's the present value of a 4-year ordinary annuity of $2, 250 per year plus an additional $3, 000 at the end of Year 4 if the interest rate is 5%?

Your cousin will sell you his coffee shop for $250, 000, with "seller financing, " at a 6.0% nominal annual rate.The terms of the loan would require you to make 12 equal end-of-month payments per year for 4 years, and then make an additional final (balloon)payment of $50, 000 at the end of the last month.What would your equal monthly payments be?

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?

Which of the following statements is CORRECT?

JG Asset Services is recommending that you invest $1, 500 in a 5-year certificate of deposit (CD)that pays 3.5% interest, compounded annually.How much will you have when the CD matures?

Suppose a State of New Mexico bond will pay $1, 000 eight years from now.If the going interest rate on these 8-year bonds is 5.5%, how much is the bond worth today?