Chapter 6 LearnSmart

Which of the following are annuities?

Monthly rent payments in a lease Installment loan payments

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.

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

Year 1 - $4,716.98 5000/(1.06) Year 2 - $5,339.98 6000/(1.06)^2 Year 3 - $4,617.91 5500/(1.06)^3

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

compounding

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

EAR

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

Mortgages Pensions

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

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

12%, compounded semiannually

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

19.56% (1.015)^12 - 1

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 though it were compounded once per year.

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

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

Which of the following payment methods amortizes a loan?

Interest plus fixed amount Fixed payments that result in a zero loan balance

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 - $4,273.50 $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

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

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

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

at the beginning of each period

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

end

For a positive stated annual interest rate and multiple compounding periods per year, the EAR is always _____ the APR.

larger than

Most investments involve:

multiple cash flows

The present value of an annuity due it equal to the present value of an __________ annuity multiplied by (1+r).

ordinary

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

present

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

tradition; legislation

Semi-annual compounding means that interest is paid _________ per year.

two times

Suppose you paid a $1,200 loan off by paying $400 in principal each year plus 10% yearly interest. How much is the second interest payment?

$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 x 0.1 = $80

If the interest rate is 10 percent per week, what is the EAR? ( Please note that 10 percent per week is not an APR. It is a weekly rate (Quoted rate/m)). Assume 52 weeks in a year.

14104%

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

9.8181

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

Annual

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

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

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.

You agree to pay back $1,100 in 4 weeks for $1,000 payday loan. Your annual percentage rate (APR) to two decimal places is __________%. (Assume weekly compounding and assume that there are 52 weeks in a year).

130.0 (1100/1000-1)x52/4 = 130%

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

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, how many months will it take to pay off your credit card?

30 months

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%

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

APY

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.

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

The present value formula for a _______ is PV = C/r, where C is the constant and regularly timed cash flow to infinity, and r is the interest rate.

perpetuity

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

principal

The original loan amount is called the:

principal

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

$3,422.24%

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

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?

$851.36

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 though it were compounded once per year.

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

$0.80 ($100 x 1.035^10) - ($100 x 1.07^5)

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

$1,000

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

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.

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

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. The borrower makes a large balloon payment at the end of the loan period. The amortization period is longer than the loan period.

You expect to receive bonuses with your job at the end of each year for the next five years. Assume you can incest 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 - $1369.40 Year 3 - $1092.03 Year 4 - $2,508.00 Year 5 - $2,200.00 Total after 5 years - $7,765.68

A traditional (non-growing) annuity consists of a(n) _________ stream of cash flows for a fixed period of time.

level

A single cash flow is also know as a:

lump sum

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

partial

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

repaid at some point in the future