Exam 4: Time Value of Money

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?

Suppose you inherited $275,000 and invested it at 8.25% per year. How much could you withdraw at the end of each of the next 20 years?

Suppose a bank offers to lend you $10,000 for 1 year on a loan contract that calls for you to make interest payments of $250.00 at the end of each QUARTER and then pay off the principal amount at the end of the year. What is the effective annual rate on the loan?

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

The payment made each period on an amortized loan is constant, and it consists of some interest and some principal. The closer we are to the end of the loan's life, the greater the percentage of the payment that will be a repayment of principal.

An investment costs $1,000 (CF at t = 0) and is expected to produce cash flows of $75 at the end of each of the next 5 years, then an additional lump sum payment of $1,000 at the end of the 5th year. What is the expected rate of return on this investment?

Your sister turned 35 today, and she is planning to save $5,000 per year for retirement, with the first deposit to be made 1 year from today. She will invest in a mutual fund that will provide a return of 8% 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 in each year after she retires? Her first withdrawal will be made at the END of her first retirement year.

You plan to borrow $75,000 at a 7% annual interest rate. 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?

You want to buy a new sports car 3 years from now, and you plan to save $4,200 per year, BEGINNING IMMEDIATELY. You will make three deposits in an account that pays 5.2% interest. Under these assumptions, how much will you have 3 years from today?

Pace Co. borrowed $25,000 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 just won the lottery, and you have a choice between receiving $3,500,000 today or a 10-year annuity of $500,000, with the first payment coming 1 year from today. What rate of return is built into the annuity?

What annual payment would you have to receive in order to earn a 7.5% rate of return on a perpetuity that has a cost of $1,250?

Suppose an investor plans to invest a given sum of money. She can earn an effective annual rate of 5% on Security A, while Security B will provide an effective annual rate of 12%. Within 11 years' time, the compounded value of Security B will be more than twice the compounded value of Security A. (Ignore risk, and assume that compounding occurs annually.)

Your uncle has $375,000 and wants to retire. He expects to live for another 25 years, and to be able to earn 7.5% on his invested funds. How much could he withdraw at the end of each of the next 25 years and end up with zero in the account?

What is the PV of an annuity due with 10 payments of $2,700 at an interest rate of 6.5%?

You want to buy a new sports car 3 years from now, and you plan to save $4,200 per year, beginning 1 year from today. You will deposit your savings in an account that pays 5.2% interest. How much will you have just after you make the third deposit, 3 years from now?

Your uncle has $375,000 and wants to retire. He expects to live for another 25 years, and he also expects to earn 7.5% on his invested funds. How much could he withdraw at the BEGINNING of each of the next 25 years and end up with zero in the account?

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.

A homeowner just obtained a 30-year amortized mortgage loan for $150,000 at a nominal annual rate of 6.5%, with 360 end-of-month payments. What percentage of the total payments made during the FIRST 3 MONTHS will go toward payment of interest?

The present value of a future sum decreases as either the discount rate or the number of periods per year increases.