Chapter 6

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

Larger than

Which are true about growing annuity?

-Cash flows grow for a finite period -Cash flows grow at a constant rate

Which are real world examples of annuities?

-Mortgages -Pensions

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

At the beginning of each period

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

EAR=1.1^52-1 =14104.29%

Which is greater, the APY or the EAR?

They are the same

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

repaid at some point in the future

Find future value of $400 per year for 10 years at 5%

=FV(.05,10,-400,0,0) 5,031.16

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

Level

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%

How frequently does continuous compounding occur?

Every instant

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

To calculate PV of cash flows:

calculate each year's PV individually (Principal/(1+r^t)) then add them

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

(1.051)^12-1= 19.56%

You agree to repay $1200 in 2 weeks for a $1000 payday loan. What is you EAR assuming there are 52 weeks in a year?

(1200/1000)^52/2-1= 11,347.55

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

-EAR= (1+.12/2)^2-1 -12% compounded semiannually

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

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

Assume interest is compounded monthly. The _______ annual rate will express this rate as though it were compounded annually.

Effective

Which is the formula for the FV of an annuity?

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

A single cash flow is also known as a:

Lump sum

Most investments involve:

Multiple cash flows

Interest paid twice a year is known as _______ compounding

Semi-annual

An investment offers $6,700 per year for 15 years, with the first payment occurring one year from now. If the required return is 6 percent, what is the value of the investment?

-Finding PV for an annuity =PV in excel =65072.07

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

100/.1=1000

The present value interest factor for an annuity with an interest rate of 8% per year over 20 years is _______

9.8181

You agree to pay back $1100 in 4 weeks for a $1000 payday loan. Your annual percentage rate APR rounded to two decimal places is _____% assume weekly compounding and 52 weeks in the year.

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

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

=1.0075^12-1 =9.38%

What is the PV of an ordinary annuity that pays $100 per year for 3 years if the interest rate is 10% per year?

=248.69

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%

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

You owe $1200 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?

=NPER(.015,-50,1200,0,0) 30 months

Which excel functions will calculate $614.46 present value of an ordinary annuity of $100 per year for 10 years at 10% per year?

=PV(.10,10,-100,0) -Make payment negative

You want to borrow $103,000 from your local bank to buy a new sailboat. You can afford to make monthly payments of $2,350, but no more. Assuming monthly compounding, what is the highest rate you can afford on a 54-month APR loan?

????

Which is the simplest form of loan?

A pure discount loan

Beginning three months from now, you want to be able to withdraw $2,300 each quarter from your bank account to cover college expenses over the next four years. If the account pays .45 percent interest per quarter, how much do you need to have in your bank account today to meet your expense needs over the next four years?

PV annuity= 2300*((1-(1/(1+r)^16)/r)=35429.66

You're funding an account that will pay your descendants the inflation adjusted equivalent of $100 per year forever. You assume inflation will be 3% per year, and you 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?

PV= C/(r-g) 2500

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 interest rate is 3%?

PV=500/(1.03)^1 =4854.37

The Maybe Pay Life Insurance Co. is trying to sell you an investment policy that will pay you and your heirs $24,000 per year forever. Suppose a sales associate told you the policy costs $469,000. At what interest rate would this be a fair deal?

PV=C/r 469,900=24,000/r solve for r =5.11%

C/r is the formula for the PV of a ______

Perpetuity

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

Tradition, legislation

You are planning to make monthly deposits of $470 into a retirement account that pays 9 percent interest compounded monthly. If your first deposit will be made one month from now, how large will your retirement account be in 35 years?

solving for FV =FV(.09/12,35*12,-470,0,0) -divide the interest rate by 12, since it is compounded monthly -For N multiply years by 12 -PV is 0