FIN 780 exam 1 chapter 4 concepts

An amount invested at compound interest earns interest on interest, whereas with simple interest, interest is not earned on interest. How much interest is earned on interest for a $10,000 investment at 7% for two years?

$.07^2 = $.0049 $10,000 x.0049 = $49

Ralph has $1,000 in an account that pays 10 percent per year. Ralph wants to give this money to his favorite charity by making three equal donations at the end of the next 3 years. How much will Ralph give to the charity each year?

$1,000/[(1 - 1/1.103)/.10] = $402.11 -Calculate the payment using the PV of an annuity at 10% for 3 years.

An interest only loan of $10,000, 8% interest rate, for 5 years would require yearly interest payments of _________.

$10,000 x.08 = $800

A 5-year $10,000 loan with a 15-year amortization period paid monthly at 10 percent, compounded monthly, will have monthly payments of ____.

$10,000/[(1 - 1/(1 + .10/12)^12x15)/(.10/12)] = $107.46

What is the future value of $100 at 10 percent simple interest for 2 years?

$100 + 2(.10 × $100) = $120

Which one of the following constitutes an infrequent annuity?

$100 once every 2 years

If you invest $100 at a stated annual rate of 10 percent compounded quarterly, how much more money will you have in 10 years than if the rate was compounded annually?

$100 × (1 + .10/4)40 - $100 × (1.10)10 = $9.13

A 20-year $100,000 loan with a 5-year amortization period paid monthly at 12 percent, compounded monthly, will have monthly payments of ____.

$100,000/[(1 - 1/(1 + .12/12)^12x20)/(.12/12)] = $1,101.09

Teresa has $100,000 in an annuity account that pays 10 percent per year. How much will she receive annually if she withdraws an equal amount over the next 20 years?

$100,000/[(1 - 1/1.10^20)/.10] = $11,746

What is the present value of $100 each year for 20 years at 10 percent per year?

$100{[1 - (1/(1.10)^20)]/0.10} = $851.36

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

$100{[1 - (1/(1.10)^3)]/.10} = $248.69

Given an interest rate of 8%, how much should you invest now in order to produce $3,000 at the end of the year?

$3,000/1+.08=$2,778

Suppose you paid off a $1,200 loan by paying $400 in principal each year plus 10 percent annual interest over a 3-year period. What is the total payment (interest plus principal) in Year 3?

$400 + ($1,200 - 800) × .10 = $440

If you invest $50 at a stated annual rate of 10 percent compounded monthly, how much more money will you have in 10 years than if the rate was compounded annually?

$50 × (1 + .10/12)120 - $50 × (1.10)10 = $5.66

Assume 12 percent annual interest is compounded semiannually on a $500 investment. What will that investment be worth after 1 year?

$500 × (1.06)^2 = $561.80

If the future value is $500 in 1 year and the interest rate is 12 percent per year, what is the present value?

$500/1.12 = $446.43

You borrow $500 and agree to pay back $575 in 2 weeks. What is the APR?

$575/$500 = 1.15 1.15 = (1 + r) r =.15, or 15% .15 x 365/14 = 3.91 = APR = 391.00%

You invest $500 at 10 percent interest per annum. At the end of 2 years with simple interest you will have ____ and with compound interest you will have ____.

$600; $605 Simple interest = 500(0.10)=$50 per year. Times two years = $100 total. Adding the original principal yields $600. With compound interest, the total is $500(1.10)2 = $605. The FV will always be higher with compound interest.

If the future value is $750 in 1 year and the interest rate is 15 percent, what is the present value?

$750/1.15 = $652.17

Assume 7 percent annual interest is compounded semiannually on a $800 investment. What will that investment be worth after 1 year?

$800 × (1.035)^2 = $856.98

Suppose you paid a $1,200 loan off by paying $400 in principal each year plus 10 percent annual interest. How much is the interest payment in the second year of the loan?

($1,200 - 400) = 800. $800 × 0.1 = $80 -You are re-paying $400 each year. Interest is computed on the principal outstanding for the year

You agree to repay $1,200 in 2 weeks for a $1,000 payday loan. What is your EAR assuming that there are 52 weeks in a year?

($1,200/$1,000)^26 - 1 = 11,347.55%

What is the difference in the future value of $100 at 7 percent interest for 5 years if the interest is compounded semiannually rather than annually?

($100 × 1.03510) - ($100 × 1..075) = $.80

A firm has cash flows of $100 at the end of years 1 - 4. How much will the present value of the firm change if the discount rate rises to 12 percent from 10 percent?

(-$13.25) -$100{[1 - (1/1.10^4)]/.10} - $100{[1 - (1/1.12^4)]/.12}

What are the implications of the time value of money concept?

-A dollar tomorrow is worth less than a dollar today -A dollar today is worth more than a dollar tomorrow

What are two ways to calculate a balloon payment?

-Amortize the loan over the loan life to find the ending balance -Find the present value of the payments remaining after the loan term

Which of the following are commonly used methods of computing an interest rate for a one-period time value of money problem in an introductory finance class?

-Calculator -Algebraic formula -Time value of money table

Which of the following are NOT ways to calculate a balloon payment?

-Find the future value of the payments for the loan term -Amortize the loan over the amortization period to get the balance

Which of the following payment methods amortizes a loan?

-Fixed payments that result in a zero loan balance -Interest plus fixed amount

Which of the following are annuities?

-Installment loan payments -Monthly rent payments in a lease

Which of the following are real-world examples of annuities?

-Mortgages -Pensions

Which of the following are ways to amortize a loan?

-Pay principal and interest every period in a fixed payment. -Pay the interest each period plus some fixed amount of the principal.

Which of the following is true about a partial amortization loan?

-The monthly payments do not fully pay off the loan by the end of the loan period. -The borrower makes a large balloon payment at the end of the loan period. -The amortization period is longer than the loan period.

Which of the following are true about the amortization of a fixed payment loan?

-The principal amount paid increases each period. -The amount of interest paid decreases each period.

In the Excel setup of a loan amortization problem, which of the following occurs?

-To find the principal payment each month, you subtract the interest payment from the total payment. -The payment is found using PMT(rate, nper,-pv, fv).

Which of the following is a means of calculating an interest rate?

-a time value of money table -a calculator -algebra

Another term for a partial amortization loan is a(n) ____ loan.

-balloon -bullet

Balloon payments on partial amortization loans are typically quite ____ because the loan balance declines slowly as the amortization period is ____ than the loan period.

-large -longer

When using a spreadsheet to determine a payment for an amortized loan, and interest rate of 8 percent would be input as

.08

The present value interest factor for a 30-year annuity with an interest rate of 10 percent per year is ______.

1 - (1/1.10^30)]/.10] = 9.4269

Rank the compounding intervals below from highest to lowest in terms of their effect on the size of a future value amount assuming all else is held constant.

1. continous 2. daily 3. semiannual 4. annual

Which formula below represents a present value factor?

1/(1 + r)t

Suppose an investment of $100 will return $148 after 10 years, what is the interest rate implied in this scenario? (round to the nearest whole percent)

100 +/- PV; 148 FV; 10 N; CPT I/Y = 3.998%

Which of the following gives an effective annual yield of 12.36 percent?

12%, compounded semiannually EAR = (1 + 0.12/2)2 -1 = 12.36%

To find the future value annuity factor from a time value of money table, read down the rows to find T = 10 and across the columns to find 10 percent. The factor where that column and row intersect is _____.

15.937 -To find the future value annuity factor from a time value of money table, read down the rows to find T = 10 and across the columns to find 10 percent. The factor where that column and row intersect is 15.937.

To find the future value annuity factor using the time value of money table, read down the rows to find T = 2, then across the columns for an interest rate of 10 percent. The intersection of that row and column will show the factor

2.100 -To find the future value annuity factor using the time value of money table, read down the rows to find T = 2, then across the columns for an interest rate of 10 percent. The intersection of that row and column will show the factor 2.10.

To find the present value of an annuity of $500 per year for 5 years at 7 percent per year using the tables, look up the present value interest factor which is ______ and multiply that by ______.

4.10020; $500 To find the present value of an annuity of $500 per year for 5 years at 7 percent per year using the tables, look up the present value interest factor which is 4.10020 and multiply that by $500.

To find the present value of an annuity of $100 per year for 10 years at 10 percent per year using the tables, look up the present value interest factor which is ______ and multiply that by ______.

6.1446; $100 To find the present value of an annuity of $100 per year for 10 years at 10 percent per year using the tables, look up the present value interest factor which is 6.1446 and multiply that by $100.

The simple interest rate of 9.99% on $1 is _____ per year and _____ total interest over 93 years. Conversely, 9.99% compounded annually for 93 years is approximately $7,030.31.

9.99 cents; $9.29 (= 93 x $.09999)

Which of the following spreadsheet (Excel) functions will calculate the $614.46 present value of an ordinary annuity of $100 per year for 10 years at 10 percent per year?

=PV(.10,10,-100,0,0)

Which of the following is a perpetuity?

A constant stream of cash flows forever

Which of the following represents an infinite and constant stream of cash flows?

A perpetuity

Which of the following will increase wealth?

A positive NPV

You borrow $100 and agree to pay back your payday loan in 2 weeks. The interest rate is 10 percent for the 2-week period. What is the APR?

APR = 52/2 × 10% = 260%

Which compounding interval will result in the lowest future value assuming everything else is held constant?

Annual

Which of the following is the formula for the present value of a growing perpetuity?

C/(r - g)

What is the general compounding formula for calculating the annual return on an investment when there is more than one compounding period in a year?

C0(1 + r/m)m

Which of the following is step one in calculating the present value of a delayed annuity?

Discount the payments back to the period prior to the start of the payments.

If you earn 8 percent a year compounded annually for 7 years on a $1,000 present value, your future value will be ____.

FV = $1,000(1.08)7 = $1,713.82

If you invest $100 at 10 percent simple interest, how much will you have in 10 years?

FV = $100 + 10($100 × .10) = $200

Assume $100 earns a stated 10 percent rate compounded quarterly. What will the value of the $100 be after one year?

FV = $100 × (1 + .10/4)4 = $110.38

If $100 earns compound interest for 2 years at 10 percent per year, the future value will be ____

FV = $100 × 1.10^2 = $121

If you invest $100 at 10 percent compounded annually, how much money will you have at the end of 3 years?

FV = $100 × 1.10^3 = $133.10

What is the future value of $100 compounded for 50 years at 10 percent annual interest?

FV = $100 × 1.10^50 = $11,739.09

The future value formula is ______.

FV = C0 × (1 + r)τ

Assume a $100 investment earns a stated interest rate of 10 percent, compounded monthly. What will be the investment value after one year?

First, find the monthly interest rate: .1/12 = .008333. Next, you can find the future value: $100 x (1+.008333)12 = $110.47

Which type of amortization is most commonly used in the real world for mortgages and car loans?

Fixed payment

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

Level; A traditional (non-growing) annuity consists of a level stream of cash flows for a fixed period of time.

If you invest $1,000 and the present value of the expected cash inflows is $1,300, then the NPV is ______

NPV = -$1,000 + 1,300 = $300

If you invest $1,000 and the present value of the incoming cash flows over the following year is $800, then the NPV is ____.

NPV = -$1,000 + 800 = -$200

If you invest $1,000 and your NPV is $200, then the present value of your future cash flows is ______.

NPV = -Cost + PV → PV = NPV + Cost PV = $200 + 1,000 = $1,200

If you invest $10,000 and your NPV is $4,000, then the present value of your future cash flows is ______.

NPV = -Cost + PV → PV = NPV + Cost PV = $4,000 + 10,000 = $14,000

If the interest rate is 10% per year, then what is today's value of $100 received one year from today?

PV = $100/1.10 = $90.91

Which one of the following is the correct formula for the one-period present value?

PV = FV/(1 + r)

An effective annual rate of 7.12 percent is equal to 7 percent compounded ______.

Semiannually EAR = (1 + .07/2)2 - 1 = 7.12%

Suppose you are using a financial spreadsheet to calculate the present of value of a yearly $250 payment for 5 years with a discount rate of 6 percent. Which of the variables should be entered as a negative?

The $250 per year payment

True or false: More money can be earned with compound interest than with simple interest.

True

True or false: The formula for the present value factor is 1/(1 + r)t.

True

At the end of 5 days, you repay your $1,000 loan plus $50 in interest. What is the EAR?

[($1,050/$1,000)365/5 -1] = 34.2224, or 3,422.24%

The present value interest factor for an annuity with an interest rate of 8 percent per year over 20 years is ____

[1-(1/1.08^20)]/.08 = 9.8181

The present value interest factor for an annuity with an interest rate of 8 percent per year over 20 years is ____.

[1-(1/1.08^20)]/.08 = 9.8181

An increase in the interest rate/discount rate will result in _____ in the NPV.

a decrease

The most common way to repay a loan is to pay ____.

a single fixed payment every period

The__________ allows for a borrowed amount to be paid off with payments that regularly reduce the

amoritized loans

The _______________ is the interest rate that ignores compounding.

annual percentage rate

An annuity in which the first payment or receipt occurs immediately is known as an ______

annuity due

An annuity due is a series of payments that are made ____.

at the beginning of each period

A lump sum payment to pay off the balance of a partially amortized loan is called a ______ payment.

balloon or bullet

The annual percentage rate is the annual interest rate without consideration of _____

compounding

The annual percentage rate is the annual interest rate without consideration of _____.

compounding

The idea behind ______ is that interest is earned on interest.

compounding

To contrast the annual percentage rate (APR) with the effective annual rate the _____ must be known.

compounding interval

A fixed payment loan has a fixed payments but the interest amount paid ______ over the life of the loan.

decreases

Which of the following refers to an annuity beginning many periods in the future?

delayed annuity

True or false: Receiving $10 today has the same value as receiving $1 today and $9 one year from now.

false

True or false: Small changes in the interest rate do not really matter when dealing with millions or billions of dollars over 30 or 40 years.

false

true or false: A balloon or bullet payment is a payment made at the beginning of the loan period.

false

A growing annuity has a(n) ____.

finite number of growing cash flows

The total value of an investment earning interest over one or more periods is known as the ______.

future value

Discounting is the process of converting ______ dollars into a ______ value.

future; present

The future value of $100 at 10 percent compounded semiannually is ______ the future value of $100 at 10 percent compounded annually.

greater than

You invest $100 today. With positive interest rates, the concept of future value implies that the future value of your $100 will be ____ $100.

greater than

A finite number of growing cash flows describes which of the following?

growing annuity

A stream of cash flows that grows at a constant rate for a finite period is called a(n) _____.

growing annuity

PV = C/(r - g) is the formula for the present value of a:

growing perpetuity.

A positive NPV will ______ wealth.

increase

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

infinite

A 3-year loan is structured as an interest-only loan with quarterly payments. Each payment during the first year will include an amount for ___.

interest only

For a positive annual percentage rate (APR) and multiple (more than one) compounding periods per year, the EAR is always ______ the APR

larger than

For a positive annual percentage rate (APR) and multiple (more than one) compounding periods per year, the EAR is always ______ the APR.

larger than

Compared to a comparable fixed payment loan, the total interest on a fixed principal loan is ___.

less

A dollar tomorrow is worth ______ a dollar today.

less than

In an infrequent annuity, the payments occur ____.

less than once a year

If reinvestment of interest or dividends does not occur, then the future value of an investment will be _____ and the realized yield will be ____ than if reinvestment had occurred.

lower; lower

A delayed annuity (or perpetuity) is one that begins ___.

many periods in the future

Compared to a comparable fixed principal loan, the total interest on a fixed payment loan is _________

more

Payments in a partial amortization loan are based on the amortization period, not the loan period. The remaining balance is then ____.

paid off in a lump sum bullet payment

The payments in a ________ amortization loan are NOT based on the life of the loan.

partial

A one-time balloon payment is associated with which of the following loan types?

partial amortization loan

When using the spreadsheet (Excel) function for finding the PV of an annuity, it's a good idea to enter the ______ as a negative value.

payment

The formula for the ______ value interest factor of an annuity is {1-[1/(1+r)t]r}1-[1/(1+r)t]r.

present

The value of a future cash flow stated in today's dollars is referred to as the _____.

present value

Amortization is the process of paying off loans by regularly reducing the _________.

principal

A 5-year loan that is repaid in a single lump sum at the end of the loan term is called a(n) _____ loan.

pure discount

The interest rate (r) used in the general compounding formula is the ______ interest rate.

quoted

Assume $10 invested today will be worth $64 in 25 years. Which one of these is the correct formula for computing the interest rate on this investment?

r = ($64/$10)1/25 - 1

Interest paid twice a year is known as ______ compounding.

semiannual

Interest earned only on your original investment is called ____, whereas interest earned on interest is called _____.

simple interest; compound interest

Balloon payments on partial amortization loans are typically quite large because ____.

the loan balance declines slowly

A borrower receives $7,500 today and repays a single lump sum in nine months. This simple form of loan is called _________.

the pure discount loan

Present value represents what an amount of money promised or expected in the future is worth ______.

today

One of the most basic principles of finance is that rational individuals prefer to receive a dollar ____ than a dollar ______.

today; tomorrow

True or false: A one-period formula for present value is PV = C1/(1 + r).

true

True or false: The first step in calculating the present value of a delayed annuity is to find the present value of the annuity one period prior to the first payment using the present value of an annuity formula.

true

True or false: The formula for finding the net present value of a cash outflow now, a positive cash flow in 1 year, and a positive cash flow in 2 years is -C0+ C1/(1 + r)1 + C2/(1 + r)2.

true

True or false: The spreadsheet (Excel) formula for calculating the present value of $100 at the end of each year for 2 years at 10 percent per year is: PV(.1,2,-100,0).

true

true or fale: A bullet payment is required in a partial amortization loan.

true

true or false: The formula for finding the present value of a cash outflow now, a positive cash flow in 1 year, and a positive cash flow in years 2 and 3 is -C0+ C1/(1 + r)1 + C2/(1 + r)2 + C3/(1 + r)3

true

Semiannual compounding means that interest is paid ______ per year.

two times

The first cash flow at the end of week 1 is $100, the second cash flow at the end of month 2 is $100, and the third cash flow at the end of year 3 is $100. This cash flow pattern is a(n) ______ type of cash flow.

uneven