Chapter 6

Which formula shows 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)]/0.10}

To find the present value of an annuity of $100 per year for 5 years at 10 percent per year using the tables, look up the present value interest factor which is ______ and multiply that by ______.

3.7908; $100

True or false: There is only one way to quote interest rates.

False There are various ways to quote rates.

Which type of amortization is most commonly used in the real world for mortgages and car loans? Multiple choice question. Fixed principal Variable period Fixed interest Fixed payment

Fixed payment

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

[1 − (1/1.1030)]/.10]

The ___ percentage rate is the interest rate charged per period multiplied by the number of periods in a year.

annual

Which of the following payment methods amortizes a loan? Multiple select question. a. Single lump sum payment b. Fixed payments that result in a zero loan balance c. Interest plus fixed amount d. Fixed interest payments only

b, c

An annuity ___ is an annuity for which the cash flows occur at the beginning of each period.

due

In the standard present and future value tables, and in all the default settings on a financial calculator, the assumption is that cash flows occur at the ___ (beginning/end) of each period.

end

Given the same APR, more frequent compounding results in _____.

higher EARs

Most investments involve _____ cash flows.

mutliple

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 Reason: If you do not enter the payment as a negative value, the result will be negative.

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

principal

The original loan amount is called the _____.

principal

What is the present value of an ordinary annuity that pays $100 per year for 20 years if the interest rate is 10 percent per year?

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

You will receive a bonus of $5,000 in one year's time, and would like to take a loan against it now. What is the formula that shows how much you can borrow if you plan to use the entire amount to pay back the loan and your interest rate is 3%?

$5,000/1.03

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,)

Which of the following is a perpetuity? Multiple choice question. a. growing stream of cash flows for a fixed period b. A constant stream of cash flows for a fixed period c. A constant stream of cash flows forever d. An undulating stream of cash flows forever

A constant stream of cash flows forever

A growing annuity has a(n) ____.

finite number of growing cash flows

The present value of a series of ___ cash flows is the amount you would need today to exactly duplicate those future cash flows.

future

When valuing cash flows, you can either value multiple cash flows or a single sum, also known as a(n) _____ sum.

lump

A single cash flow is also known as a:

lump sum

The loan balance on partial amortization loans declines so slowly because the ___.

payments are mostly interest

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

present

With interest-only loans that are not perpetuities, the entire principal is _____.

repaid at some point in the future

To use a present value of an annuity table to find the present value of an annuity factor, search the ______ for the number of periods and the ______ for the rate.

row; column

Interest paid twice a year is known as ______ compounding.

semiannual

Because of __________ and _________, interest rates are often quoted in many different ways.

tradition; legislation

The formula for the present value interest factor for annuities is: Annuity present value factor = {1-[1/(1+r)^t]} / r.

True

True or false: A fixed payment loan is most common for consumers.

True

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

[1 − (1/1.0820)]/.08 or 9.8181 Reason: [1 − (1/1.0820)]/.08

___ is the process of paying off loans by regularly reducing the principal.

amortization

The future value factor for a(n) ___ is found by taking the future value factor and subtracting one, then dividing this number by the interest rate.

annuity

The present value of a(n) of C dollars per period for t periods when the rate of return or interest rate, r, is given by: C × (1 − [1/(1 + r)t]r/)

annuity

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

at the beginning

Which of the following are real-world examples of annuities? Multiple select question. Mortgages Common stock dividends Pensions

Mortgages Pensions

How frequently does continuous compounding occur?

Every instant

Which of the following is the formula for the future value of an annuity?

FV=C{[(1+r)^t -1]/r}

In almost all multiple cash flow calculations, it is implicitly assumed that the cash flows occur at the _____ of each period.

end

The present value of a series of future cash flows is the amount you would need today to _____.

exactly duplicate those future cash flows.

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

infinite

One method of calculating future values for multiple cash flows is to compound the accumulated balance forward _____ at a time.

one year

A typical investment has a large cash ___ (inflow/outflow) at the beginning and then a cash ___ (inflows/outflows) for many years.

outflow; inflow

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 loan balance on ___ amortization loans declines so slowly because the payments are mostly interest.

partial

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

partial

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?

$402.11 Reason: Correct. Calculate the payment using the PV of an annuity at 10 percent for 3 years. $1,000/[(1 − 1/1.103)/0.10] = $402.11.

Which of the following is equal to an effective annual rate of 12.36 percent?

12%, compounded semiannually Reason: For quarterly compounding, the EAR = (1+0.12/4)4 - 1= 12.55%. For 12% compounded semiannually, EAR = (1 + 0.12/2)2 -1 = 12.36%

Match the type of rate with its definition. APR EAR The interest rate per period multiplied by the number of periods in the year. The interest rate stated as though it were compounded once per year.

APR <->The interest rate per period multiplied by the number of periods in the year. EAR<->The interest rate stated as though it were compounded once per year.

Which of the following are annuities? Multiple select question. Installment loan payments Monthly grocery bill Monthly rent payments in a lease Tips to a waiter

Installment loan payments Monthly rent payments in a lease

Which of the following is the simplest form of loan?

Pure discount loan The borrower receives money today and repays a single lump sum (principal and interest) at a future time.

Which of the following are ways to amortize a loan? Multiple select question. a. Pay principal and interest every period in a fixed payment. b. Pay the interest each period plus some fixed amount of the principal. c. Pay both interest and principal in one lump sum at maturity d. Pay only interest every period and pay the principal off at maturity

a, b

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 future value of an annuity? a. FV = C((1− 1/ (1+r)^t / r) b. FV = C((1+r)^t −1 / r) c. FV = C((1−r)^t +1 / r)

b

Which of the following are true about a partial amortization loan? Multiple select question. a. The amortization period is shorter than the loan period. b. The borrower makes a large balloon payment at the end of the loan period. c. The amortization period is longer than the loan period. d. The monthly payments do not fully pay off the loan by the end of the loan period. e. The monthly payment is based on a longer amortization period than the maturity of the loan.

b, c, d, e

Which of the following is true about a growing annuity? Multiple select question. a. The cash flows grow at an irregular rate. b. The cash flows grow at a constant rate. c. The cash flows grow for an infinite period. d. The cash flows grow for a finite period.

b, d

Which of the following processes can be used to calculate future value for multiple cash flows? Multiple select question. a. Discount all of the cash flows back to Year 0 b. Compound the accumulated balance forward one year at a time c. Find the future value of a single lump sum amount d. Calculate the future value of each cash flow first and then add them up

b, d

Which of the following payment methods amortizes a loan? Multiple select question. a. Single lump sum payment b. Fixed interest payments only c. Interest plus fixed amount d. Fixed payments that result in a zero loan balance

c, d