Chapter 6 Questions

you agree to pay back $1,100 in 4 week for a $1,000 payday loan--your annual percentage rate ( APR ) rounded to two decimal places is ---%. ( assume weekly compounding & assume there are 52 weeks a year)

= ( 1,100/1000-1) * 52/4 = 130%

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

FV = C ( (1+r)^t-1/r) C is cash flow per period i is rate of interest n is the frequency of payments

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

Larger than

A single cash flow is also known as a

Lump Sum

Another common name for the effective annual rate is the annual percentage

Yield

Most investments involve

multiple cash flows

Semi annual compounding means that interest is paid

two times

The original loan amount is called the

the principal amount of the loan originally made by each lender to Borrower

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

(( $1050 / $1000) ^ (365/5) -1 = 3,422.24%

Which of the following are annuities?

1. installment loan payments 2. monthly rent payments in a lease

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

1. monthly payment is based on a longer amortization period than the maturity of the loan ( in a partial amortization loan, the amortization period is longer than the loan period, so that 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) 2. monthly payments do not fully pay off the loan by the end of the loan period 3. borrower makes a large balloon payment at the end of the loan period 4. the amortization period is longer than the loan period

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%

1. the present value of the Year 1 cash flow $5,000/1.17 2. present value of the Year 2 Cash flow $4,300/ (1.17)^3 3. Present value of the Year 3 Cash Flow $5,000/(1.17)^3 Now, calculate them

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

1. the principal amount paid increases each period --sidenote--- the amount of interest paid decreases each period. the schedule on page 175 illustrated this reduction ----------- 2. amount of interest paid decreases each period

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

1. to find the principal payment each month, you subtract the interest payment from the total payment 2. the payment is found using PMT ( rate, nper, -pv, fv )

You expect to receive bonuses at your job @ end of each year for next five years. assume you can invest all 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. yr 1 %500 yr 2 $1,200 yr 3 $1,000 yr 4 $2,400 yr 5 $2,200

yr 1 $596.26 how to: Future Value factor for year 1 = (1+4.5%)^4 yr 2 $1,369.40 how to (1+4.5%)^3 ( see the pattern ? follow through) yr 3 $1,092.03 yr 4 $2, 508.00 yr 5 $2,200.00 Total after 5 years $7,765.68

which of the following is true about a growing annuity?

1. cash flows grow for a finite period 2. cash flows grow at a constant rate

which of the following are ways to amortize a loan?

1. pay principal and interest every period in a fixed payment 2. pay the interest each period plus some fixed amount of the principal

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

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

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?

SOLVE $100 * { 1-(1/1.10)^20)] / .10 = 851.36

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

if the stated interest rate is 10 percent, what is the EAR if interest is compounded monthly?

apply the EAR formula EAR = ( 1 + i/n) ^n -1 i= stated annual interest rate n= number of compounding periods = 10.47%

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

how to 100/(7%-3%) = $2,500

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

investment value after 1 year? $110.47 FV = $100*(1+0.10/12)^12

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?

$80 you are re paying $400 each year. interest is computed on the principal outstanding for the year, which is ($1,200 - 400 ) = 800. $800 * 0.1 = $80

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

1. compound the accumulated balance forward one year at a time 2. calculate the future value of each cash flow first and then add them up

What are two ways to calculate a balloon payment?

1. find the present value of the payments remaining after the loan term 2. amortize the loan over the loan life to find the ending balance

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

present

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

present value of an annuity due is: (1+r) * ( PV of an ordinary annuity )

amortization is the process of paying off loans by regularly reducing the -----

principal

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 percent value, then match the total amount you should pay for the investment today to the appropriate box. yr 1 %5,000 yr 2 $6,000 yr 3 $5,500

yr 1 $4,716.98 ---- 5,000/(1.06) yr 2 $5, 339.98 ---- 6000/(1.06)^2 yr 3 $4617.91 ------- 5500/(1.06)^3 yr 4 $14,674.87 ----you should not pay more than the PV of the cash flows, which the sum of the discounted cash flows. ( adding up yr 1,2, & 3 )

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

1. a consol ( bond that pays interest only and does not mature ) 2. cash flows from a product whose sales are expected to remain constant forever 3. preferred stock

Matching 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 though it were compounded once per year

The general formula for the ---is (1+r/m)^m-1

EAR

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

in almost all multiple cash flow calculations, it is implicitly assumed that the cash flows occur at the

end

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

present value formula for an ----is PV = C/r, where C is the constant & regularly times cash flow to infinity, and r is the interest rate

perpetuity

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

100/.1= 1000

if the interest rate is 10 percent per week, what is the EAR? ( please not that 10 percent per week is not an APR. it is a weekly rate ( quoted rate/m--assume 52 weeks in a year

EAR = 1.1^52-1 = 14104.29%

you are planning to buy a CD for $1,352. you'll receive $1,500 in 2 years. use a financial calculator to find the interest rate you will receive on that investment, assuming annual compounding

N number of Periods I/Y interest rate per period PV present value PMT payment amount each period FV future value N = 2 FV = 1500 PV = -1352 PMT = 0 NOW CPT I /Y = 5.33%

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

compounding

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----& multiply that by ----

number of period on the table = 5; interest rate of 10% = 3.7908 present value interest value = $100