Smartbook 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

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

$110.38 FV = $100 x (1+0.10/4)^4

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

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

$5031.16

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?

11,347.55%

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

12% compounded semiannually

You agree to pay back $1,000 in 4 weeks for a $1,000 payday loan. Your annual percentage rate (APR) rounded to two decimal places is ___% (Assume weekly compounding and assume that there are 52 weeks in a year)

130.0 (1100/1000-1) x 52/4 = 130%

If the interest rate is 10% per week, what is the EAR?

14104% EAR = 1.10^52 - 1

A credit card charges 18% interest per year (APR) (1.5% each month). What is the EAR?

19.56% (1.015)^12 - 1 = 19.56%

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? (Assume 365 days a year)

260.71%

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

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

The annuity present value factor for a 30-year annuity with an interest rate of 10% per year is ___

9.4269

Match the type of rate with its definition: 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

Another common term for the effective annual rate (EAR) is the:

APY

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

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

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

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

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

T/F - The formula for the present value interest factor for annuities is Annuity present value factor = (1-(1/(1+r)^t)/r

True

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 - $5000 YEAR 2 - $6000 YEAR 3 - $5500

YEAR 1 - $4716.98 YEAR 2 - $5339.98 YEAR 3 - $4617.91 amount you should pay for investment - $14674.87

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%

YEAR 1 PV - $4273.50 YEAR 2 PV - $3141.21 YEAR 3 PV - $3121.85

You expect to receive bonuses with your job at the end of each year for the next five years. Assume you can invest all of our 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 - $1369.40 Year 3 - $1092.03 Year 4 - $2508.00 Year 5 - $2200.00 Total after 5 years - $7765.68

An annuity due is a series of payments that are made ___

at the beginning of each period

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

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

When calculating the future value of multiple cash flows using a spreadsheet, you must:

calculate the future value of each cash flow then add the compounded values together

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

compounding

In almost all multiple cash flow calculations, its implicitly assumed that the cash flows occur at the ___ of each period

end

Which of the following payment methods amortizes a loan?

fixed payments that result in a zero loan balance interest plus fixed amount

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

infinite

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 traditional (non-growing) annuity consists of a ___ stream of cash flows for a fixed period of time

level

A single cash flow is also known as a:

lump sum

Which of the following are annuities?

monthly rent payments in a lease installment loan payments

Most investment involve:

multiple cash flows

Most investments involve:

multiple cash flows

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)^t] / r

present

The original loan amount is called the:

principal

Interest paid twice a year is known as ___ compounding

semi-annual

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

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

tradition legislation

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

yield

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

$1000

What is the present value 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 an annuity due is:

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

To find the present value of an annuity of $100 per year using the tables, look up the present value interest factor which is ___ and multiply that by ___

3.7908 $100

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

5.33%

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, and you expect the account to earn 7% per year. How much do you need to put in the account today to ensure your gift will continue forever?

$2,500 This is a growing perpetuity, because you want the $100 to grow at the inflation rate every year. So its value is PV = C/(r-g)=100/(0.07-0.03)=2,500 today Value here ($1428.57) is the value of the perpetuity if it does not grow

Your bank quotes a 9% APR on your car loan (.75 percent interest each month). What is the EAR?

9.38% 1.0075^12 - 1 = 9.38%

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% per year?

=PV(0.10,10,-100,0)