Chapter 6

What is the formula to calculate the future value of an annuity due of $100 per year for 10 years at 10 percent per year?

$100[(1.1010 − 1)/0.10][1.10]

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}

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}

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

12%, compounded semiannually

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 should be valued using a perpetuity formula?

A consol (bond that pays interest only and does not mature). Cash flows from a product whose sales are expected to remain constant forever. Preferred stock.

Which of the following is a perpetuity?

A constant stream of cash flows forever

Which of the following is the simplest form of loan?

A pure discount loan

APR? EAR?

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.

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

Amortization

Which of the following processes can be used to calculate future value for multiple cash flows?

Compound the accumulated balance forward one year at a time. Calculate the future value of each cash flow first and then add them up.

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

FV = C((1+r)t−1r)

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

False

What are two ways to calculate a balloon payment?

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

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

Future

Which of the following show the inputs you would use in a financial calculator to compute the present value of $100 per year for 30 years if the discount rate is 5%?

In your financial calculator, enter 100 for PMT, 30 for N, and 5 for I/Y. Solve for PV.

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

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

Mortgages Pensions

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

Partial

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

Which of the following is true about a growing annuity?

The cash flows grow for a finite period. The cash flows grow at a constant rate.

The formula for the present value interest factor for annuities is: Annuity present value factor = {1-[1/(1+r)t]}r1-[1/(1+r)t]r.

True

What is formula to calculate the present value of an annuity that makes payments of $100 per year for 10 years if the first payment is made immediately and the discount rate is 10 percent per year?

$100[(1 − 1/1.10^10)/0.10][1.10]

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

Annual

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

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

Due

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

End

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

Which of the following show the steps you would apply using a financial calculator to find the future value of an annuity of $100 per year for 10 years at 15%?

Enter 100 for PMT, 10 for N, and 15 for I/Y. Solve for FV.

Which of the following show the steps you would apply using a financial calculator to find the future value of an annuity of $400 per year for 10 years at 5%?

Enter 400 for PMT, 10 for N, and 5 for I/Y. Solve for FV.

You owe $1,200 on your credit card, which charges 1.5% per month. If you pay $50 per month starting at the end of this month, which of the following show the steps you will apply using a financial calculator to solve for the number of months will it take to pay off your credit card?

Enter −50 for PMT, 1,200 for PV, and 1.5 for I/Y. Solve for N.

Which of the following are annuities?

Monthly rent payments in a lease Installment loan payments

When using a financial calculator to determine the number of payments on a loan, you may use the inputs I/Y, PMT, and PV to solve for _____.

N

You may use which of the following sets of inputs together to solve for the present value of an annuity using a financial calculator?

N, I/Y, PMT, PV

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

One year

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 original loan amount is called the _____.

Principal

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

payments are mostly interest

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

principal

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

repaid at some point in the future

Interest paid twice a year is known as ______ compounding.

semiannual

Semiannual compounding means that interest is paid ______ per year.

two times

The present value of an annuity due is equal to the present value of a(an) ______ annuity multiplied by (1 + r).

ordinary

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

tradition; legislation

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

The formula for the present value of an annuity due is _____.

(1 + r) × (PV of an ordinary annuity)

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

exactly duplicate those future cash flows

A growing annuity has a(n) ____.

finite number of growing cash flows

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

higher EARs