Ch. 5: Part 2

How much is $100 at the end of each year forever at 10% interest worth today?

$1,000 Rationale: 100/0.10= 1,000

How many years will it take you to double your money if you invest it in an account paying an annual compounded return of 12 percent?

6.12 Rationale: 2=(1.12)^x Log(2)=X*Log(1.12) Log(2)/Log(1.12)=x x=6.12

The present value of an annuity of $1 per period is called the ______________.

annuity factor

A traditional (non-growing) annuity consists of a(n) ________ stream of cash flows for a fixed period of time.

fixed

A perpetuity is a constant stream of cash flows for a(n) ______ period of time.

infinite

A series of level payments that begins immediately for a specified period of time is called a(n):

annuity due

C/r is the formula for the present value of a(n) ____.

perpetuity

To use your financial calculator to solve annuity problems, you use the _____ key for entry of the constant payment C.

pmt

In Excel, cash inflows are recognized as ______ values and cash outflows are recognized as ______ values. Interest rates should be entered as ______.

positive, negative, decimals

The future value of an annuity that lasts n years is equal to

the present value allowed to grow n years.

An annuity due is a series of level payments that begin ____.

immediately

The present value of an annuity due is equal to the:

present value of an ordinary annuity x (1+r)

Find the future value of an annuity of $100 per year for 10 years at 10 percent per year.

$1,593.75 Rationale: First, find the PV by using the 10 year annuity factor: PV = $100 x 10 year annuity factor = $100 x [1/.1 - 1/.1x(1.1)10]= $614.46 To find the future value, multiply $614.46 x (1.1)10= $1,593.75.

A fixed stream of cash flows that ends after a specified number of years is called a(n):

annuity

Real-world investments often involve many payments received or paid over time. Managers refer to this as a ___________________.

stream of cash flows

Today you deposit $1000 in an account paying 6% interest. At the end of years 1, 2 and 3 you will deposit $100 in that account. What is the present value of that stream of cash flows?

$1,267.30 Rationale: $1000 + $100/(1.06)1 + $100/(1.06)2 + $100/(1.06)3 = $1,267.30

Today you deposit $1000 in an account paying 6% interest. At the end of years 1, 2 and 3 you will deposit $100 in that account. How much will you have at the end of year 4?

$1,599.94 Rationale: $1000(1.06)^4 + $100(1.06)^3 + $100(1.06)^2 + $100(1.06)^1 = $1,599.94

$200 at the end of each year forever at 10% per year is worth how much today?

$2,000 Rationale: $200/0.10 = $2,000

Your insurance agent wants to sell you an annuity consisting of 20 equal end of year payments of $10,000 each, starting at the end of this year. Your desired rate of return for investments of this type is 7 percent. What is the most you would pay for this annuity today?

$105,940.14 Rationale: PV = 10000[1/0.07 - 1/0.07(1.07)20] = 105,940.14

What is the future value of a series of $2000 end of year deposits into an IRA account paying 5 percent interest, over a period of 35 years? Use your financial calculator.

$180,640.61 Rationale: n=35,i=5,PV=0,PMT= 2000, compute FV=180640.61

What is the present value of an ordinary annuity that pays $100 per year for three years if the interest rate is 10% per year?

$248.69 Rationale: 100[(1/.10)-(1/(.10(1.10)3))] = 248.69

Your opened an IRA 35 years ago, making an initial deposit, but no additional deposits after that. Today you have $250,000 in that account. Assume you earned 5% per year. What was the amount of that initial deposit?

$45,322.57 Rationale: FV=250,000, n=35, i=5, PMT=0, compute PV= -45,322.57

Match the financial calculator keys below with their correct functions: n i PV FV PMT

n: number of periods i: interest rate expressed as a percentage PV: present value FV: future value PMT: constant recurring payment

The interest rate on the financial calculator is expressed as a

percentage

The present value formula for a(n) ______ is PV = C/r, where C is the constant and regularly timed cash flow to infinity, and r is the interest rate.

perpetuity

What is the present value of an annuity consisting of 20 end of year payments of $500 when the interest rate is 11 percent? Use your financial calculator.

$3,981.66 Rationale: n=20,i=11,FV=0,PMT=500, compute PV = 3981.66 (1/r-1/r(1+r)^time)x500

You will receive $100 in 1 year, $200 in 2 years and $300 in 3 years. If you can earn a 7.5% rate of interest, what is the present value of this stream of cash flows? (Please note that you receive nothing immediately - there is no initial payment).

$507.58 Rationale: $100/(1.075)1 + $200/(1.075)2 + $300/(1.075)3 = $507.58

You put $100 in the bank now, $200 in the bank a year from now, and $300 in the bank in two years. How much money will you have available 3 years from now if you earn a 7.5% rate of interest? (Calculate the future value of this stream of cash flows. Refer to Example 5.6.)

$677.85 Rationale: $100 x (1.075)3 + $200 x (1.075)2 + $300 x (1.075) = $677.85

What is the present value of an annuity consisting of 100 end of year payments of $50,000 when the interest rate is 6 percent? Use your financial calculator.

$830,877.31 Rationale: n=100,i=6,PMT=50000,fv FV=0, compute FV=830877.31 (1/r-1/r(1+r)^time)x50000

The present value of $100 paid annually at year end for 20 years at 10% per year is:

$851.36 Rationale: 100[(1/.10)-(1/(.10(1.10)20))] = 851.36

Which of the following is the correct equation for the present value of an annuity with regular payment C for t periods at interest rate r?

PV = C[1/r - 1/r(1+r)t]

True or false: The time value of money functions that are provided by your financial calculator are also available as functions in an Excel spreadsheet.

True

Which of the following are annuities?

Yearly lease payments Annual installment loan payments

An ordinary annuity is a series of level payments that begin ____.

at the end of one payment period

If interest rates go up, the present value of a perpetuity will ______.

decrease

If the interest rate is greater than zero, the present value of an annuity due is always ______ an ordinary annuity.

greater than

If interest rates go down, the present value of a perpetuity will _____________.

increase

A stream of cash flows means that ________.

payments are made over time

Which of the following is a perpetuity?

A constant stream of cash flows forever