FIN 3320 CHAPTER 6

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

$0.80

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

$1,000 (100/.1)

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

$107.46

You have decided to fund an an account that will pay your descendants that inflation-adjusted equivalent of $100 per year forever. You assume inflation will equal 3% per year, and expect the account to earn 7% per year. How much do you need to put in the bank today to ensure your gift will continue forever?

$2,500

The general formula for the EAR Is:

(1+r/m)^m-1

Which of the following are true abut a partial amortization loan?

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

Which of the following should be valued using a perpetuity formula?

-preferred stock -cash flows from a product whose sales are expected to remain constant forever -a consol (bond that pays interest only and does not mature)

If the interest rate is 10 percent per week, what is the EAR? Assume 52 weeks in a year.

14104%

To find the present value of an annuity of $100 per year for 5 years at 10% per year using the tables, find a present value factor of ________ and multiply it by ___________.

3.7908;$100

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

3422.24%

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

400+(1200-800)*.10=480

Ralph has $1000 in an account that pays 10% per year. Ralph wants to give his 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

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

At the beginning of each period

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

FV= $100 X (1+.10/4)^4= 110.38

If C=$100, g=10%, r=15%, and t=2 years, then what is the PV of this growing annuity?

PV = 100 x [1 - (1.1/1.15)^2 ] // .15 - .1= 100 x 1.701323= $170.13

You will receive a bonus of $5000 in one year and would like to take a loan against it now. How much can you borrow if you plan to use the entire amount to pay back the loan and your

PV=500/(1.03)^1= 4854.37

You expect to receive bonuses with your job each year for the next five years. Assume you can invest all of your bonuses at 4.5% and the bonuses are as shown below, match each amount to its future value at the end of the five years, then match the total to the appropriate box. Year 1: $500/ Year 2: $1,200 /Year 3: $1,000/ Year 4: $2,400/ Year 5: $2,200

Year 1: $596.26 Year 2: $1,369.40 Year 3: $1,092.03 Year 4: $2,508.00 Year 5: $2,200.00 Total after 5 years: $7,765.68

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

annual

When calculating the present value of multiple cash flows using a spreadsheet, you must ---

calculate the present value of each cash flow then add the discounted values together

The effective annual rate (EAR) takes into account the __ of the interest that occurs within a year.

compounding

One example of a perpetuity is a British ----

consol

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

larger than

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

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

present

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

principal

the original loan amount is called the:

principal

Interest paid twice a year is known as _____ compounding.

semi-annual

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

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

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

-pensions -mortgages -leases

You borrow $100 and agree to pay back your payday loan in 2 weeks for 10% interest over that 2 week period. What is your APR?

260.71%

You are planning to buy a CD for $1,352. You will receive $1500 in 2 years. Use a financial calculator to find the interest rate you will receive on that investment, assuming annual compounding.

5.33%

An APR of 9% with continuous compounding gives an EAR of

9.42%

Which is the simplest form of loan?

A pure discount loan

Match the type of rate with its definition.

APR= The interest rate per period multiplied by the number of periods in the year.EAR= The interest rate stated as thought it were compounded once per year.

another term for EAR

APY

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

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

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

FV= C(1+r^t-1/r)

With interest-only loans that are NOT perpetuities, the entire principal is:

Repaid at some point in the future

which of the following is true about a growing annuity?

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

Payday Loans allow you to

borrow now and repay later

What is 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% per year?

$675.90

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

$851.36

The formula for the present value of annuity due is:

(1 + r) x (PV of an ordinary annuity)

Suppose you need $5,000 in one year, $4,300 in two years, and $5,000 in three years. Match each present value amount to the corresponding cash flow assuming a discount rate of 17%

* Present value of the Year 1 Cash Flow= $4,273.17 [$5,000/1.17] * Present value of the Year 2 Cash Flow= $3,141.21 [$4,300/(1.17)^2] *Present value of the Year 3 Cash Flow= $3,121.85 [$5,000/(1.17)^3]

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 true about the amortization of a fixed payment loan?

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

The annuity PV factor for a 30 year annuity with an interest rate of 10% per year is __________

PVIFA= {1-(1/1.1^30)}/.10= 9.4269

Which of the following are ways to amortize loan?

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

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

balloon or bullet

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

less

A single cash flow is also known as:

lump sum

Most investments involve:

multiple cash flows

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

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

semiannually

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

tradition; legislation

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 an ________ cash flow.

uneven

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

payments are mostly interest

You are considering an investment that will earn the following cash flows over the next three years. You expect to earn 6% return on the investment. Match each cash flow with its present value, then match the total amount you should pay for the investment today to the appropriate box. Year 1 Year 2 Year 3 Amount you should pay for the investment

$4,716.98; 5,339.98; 4,617.91; 14,674.87

Use your financial calculator to find the future value of an annuity of $400 per year for 10 years at 5%.

$5,031.16

Amy took out a mortgage of $100,000 at 4.5% with monthly payments for 30 years. What is her payment to principal and interest each month?

$506.69

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

end

How frequently does continuous compounding occur?

every instant

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

fixed payment

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

greater than

Given the same APR, more frequent compounding results in ----

higher EARs