Fin Ch.5

Approximately how much must be saved for retirement in order to withdraw $100,000 per year for the next 25 years if the balance earns 8% annually, the first payment occurs one year from now?

$1,067,477.62

How much more is a perpetuity of $1,000 worth than an annuity of the same amount for 20 years? Assume an interest rate of 10% and cash flows at the end of each period.

$1,486.44

You invested $1,200 three years ago. During the three years, you earned annual rates of return of 4.8%, 9.2%, and 11.6%. What is the value of this investment today?

$1,532.60

Three thousand dollars is deposited into an account paying 10% annually to provide three annual withdrawals of $1,206.34 beginning in one year. How much remains in the account after the second payment has been withdrawn?

$1.096.69

You will be receiving cash flows of: $1,000 today, $2,000 at end of year 1, $4,000 at end of year 3, and $6,000 at end of year 5. What is the present value of these cash flows at an interest rate of 7%?

$10,412.27

What is the present value of $100 to be deposited today into an account paying 8% compounded semiannually for 2 years?

$100.00

How much interest can be accumulated during one year on a $1,000 deposit paying continuously compounded interest at an APR of 10%?

$105.17

How much interest will be earned in the next year on an investment paying 12% compounded annually if $100 was just credited to the account for interest?

$112

A loan officer states, "Thousands of dollars can be saved by switching to a 15-year mortgage from a 30-year mortgage." Calculate the difference in payments on a 30-year mortgage at 9% interest versus a 15-year mortgage with 8.5% interest. Both mortgages are for $100,000 and have monthly payments. What is the difference in total dollars that will be paid to the lender under each loan? (Round the monthly payment amounts to 2 decimal places.)

$112,410

What is the present value of a five-period annuity of $3,000 if the interest rate per period is 12% and the first payment is made today?

$12,112.05

With $1.5 million in an account expected to earn 8% annually over the retiree's 30 years of life expectancy, what annual annuity can be withdrawn, beginning today?

$123,371.44

What is the future value of $10,000 on deposit for 5 years at 6% simple interest?

$13,000.00

How much will accumulate in an account with an initial deposit of $100, and which earns 10% interest compounded quarterly for 3 years?

$134.49

How much interest will be earned in an account into which $1,000 is deposited for one year with continuous compounding at a 13% rate?

$138.83

Eighteen years from now, 4 years of college are expected to cost $150,000. How much more must be deposited into an account today to fund this expense if you could only earn 8% rather than the 11% you had hoped to earn on your savings?

$14,614.03

Your real estate agent mentions that homes in your price range require a payment of $1,200 per month for 30 years at 9% interest. What is the size of the mortgage with these terms?

$149,138.24

$50,000 is borrowed, to be repaid in three equal, annual payments with 10% interest. Approximately how much principal is amortized with the first payment?

$15,105.74

Miller's Hardware plans on saving $42,000, $54,000, and $58,000 at the end of each year for the next three years, respectively. How much will the firm have saved at the end of the three years if it can earn 4.5% on its savings?

$160,295.05

Prizes are often not "worth" as much as claimed. Place a value on a prize of $5,000,000 that is to be received in equal payments over 20 years, with the first payment beginning today. Assume an interest rate of 7%.

$2,833,898.81

If $120,000 is borrowed for a home mortgage, to be repaid at 9% interest over 30 years with monthly payments of $965.55, how much interest is paid over the life of the loan?

$227,598

What is the present value of your trust fund if you have projected that it will provide you with $50,000 of your 30th birthday (7 years from today) and it earns 10% compounded annually?

$25,657.91

A corporation has promised to pay $1,000 20 years from today for each bond sold now. No interest will be paid on the bonds during the 20 years, and the bonds are discounted at an interest rate of 7%, compounded semiannually. Approximately how much should an investor pay for each bond?

$252.57

You're ready to make the last of four equal, annual payments on a $1,000 loan with a 10% interest rate. If the amount of the payment is $315.47, how much of that payment is accrued interest?

$28.68

What is the present value of a four-year annuity of $100 per year that begins 2 years from today if the discount rate is 9%?

$297.22

How much must be saved at the end of each year for the next 10 years in order to accumulate $50,000, if you can earn 9% annually? Assume you contribute the same amount to your saving every year.

$3,291.00

How much must be invested today in order to generate a 5-year annuity of $1,000 per year, with the first payment 1 year from today, at an interest rate of 12%?

$3,604.78

How much must be deposited today in an account earning 6% annually to accumulate a 20% down payment to use in purchasing a car one year from now, assuming that the car's current price is $20,000 and inflation will be 4%?

$3,924.53

Assume the total expense for your current year in college equals $20,000. How much would your parents have needed to invest 21 years ago in an account paying 8% compounded annually to cover this amount?

$3,973.11

A perpetuity of $5,000 per year beginning today is said to offer a 15% interest rate. What is its present value?

$38,333.33

Approximately how much should be accumulated by the beginning of retirement to provide a $2,500 monthly check that will last for 25 years, during which time the fund will earn 6% interest with monthly compounding?

$388,017.16

The salesperson offers, "Buy this new car for $25,000 cash or, with an appropriate down payment, pay $500 per month for 48 months at 8% interest." Assuming that the salesperson does not offer a free lunch, calculate the "appropriate" down payment.

$4,519.04

What is the present value of the following payment stream, discounted at 8% annually: $1,000 at the end of year 1, $2,000 at the end of year 2, and $3,000 at the end of year 3?

$5,002.10

How much more would you be willing to pay today for an investment offering $10,000 in 4 years rather than in 5 years? Your discount rate is 8%.

$544.47

Your car loan requires payment of $200 per month for the first year and payments of $400 per month during the second year. The annual interest rate is 12% and payments begin in one month. What is the present value of this 2-year loan?

$6,246.34

On the day you retire you have $1,000,000 saved. You expect to live another 25 years during which time you expect to earn 6,18% on your savings while inflation averages 2.5% annually. Assume you want to spend the same amount each year in real terms and die the day you spend your last dime. What real amount will you be able to spend each year?

$61,334.36

The present value of an annuity stream of $100 per year is $614 when valued at a 10% rate. By approximately how much would the value change if these were annuities due?

$61.40

How much can be accumulated for retirement if $2,000 is deposited annually, beginning 1 year from today, and the account earns 9% interest compounded annually for 40 years?

$675,764.89

What will be the monthly payment on a home mortgage of $75,000 at 12% interest, to be amortized over 30 years?

$771.46

How much interest is earned in just the third year on a $1,000 deposit that earns 7% interest compounded annually?

$80.14

Lester's just signed a contract that will provide the firm with annual cash inflows of $28,000, $35,000, and $42,000 over the next three years with the first payment of $28,000 occurring one year from today. What is this contract worth today at a discount rate of 7.25%?

$90,580.55

What is the discount factor for $1 to be received in 5 years at a discount rate of 8%?

.6806

What is the annually compounded rate of interest on an account with an APR of 10% and monthly compounding?

10.47%

What is the APR on a loan with an effective annual rate of 15.26% and weekly compounding if interest?

14.22%

How long must one wait (to the nearest year) for an initial investment of $1,000 to triple in value if the investment earns 8% compounded annually?

14.27 years

"Give me $5,000 today and I'll return $10,000 to you in 5 years," offers investment broker. To the nearest percent, what annual interest rate is being offered?

14.87%

If the effective annual rate of interest is known to be 16.08% on a debt that has quarterly payments, what is the annual percentage rate?

15.19%

A credit card account that charges interest at the rate of 1.25% per month would have an annually compounded rate of ___ and an APR of ___.

16.08%; 15%

What is the APR on a loan that charges interest at the rate of 1.4% per month?

16.80%

After reading the fine print in your credit card agreement, you find that the "low" interest rate is actually an 18% APR, or 1.5% per month. What is the effective annual rate?

19.56%

If the future value of an annuity due is $25,000 and $24,000 is the future value of an ordinary annuity that is otherwise similar to the annuity due, what is the implied discount rate?

4.17%

If inflation in Wonderland averaged about 3% per month in 2013, what was the annual rate of inflation?

42.58%

What will be the approximate population of the United States, if its current population of 300 million grows at a compound rate of 2% annually for 25 years?

492 million

What is the expected real rate of interest for an account that offers a 12% nominal rate of return when the rate of inflation is 6% annually?

5.66%

What APR is being earned on a deposit of $5,000 made 10 years ago today if the deposit is worth $9,848.21 today? The deposit pays interest semiannually.

6.89%

Your retirement account has a current balance of $50,000. What interest rate would need to be earned in order to accumulate a total of $1,000,000 in 30 years, by adding $6,000 annually?

7.24%

In calculating the present value of $1,000 to be received 5 years from today, the discount factor has been calculated to be .7008. What is the apparent interest rate?

7.37%

If a borrower promises to pay you $1,900 nine years from now in return for a loan of $1,000 today, what effective annual interest rate is being offered if interest is compounded annually?

7.39%

Would you prefer a savings account that paid 7% interest compounded quarterly, 6.8% compounded monthly, 7.2% compounded weekly, or an account that paid 7.5% with annual compounding?

7.5% compounded annually

What is the minimum nominal rate of return that you should accept if you require a 4% real rate of return and the rate of inflation is expected to average 3.5% during the investment period?

7.64%

Would a depositor prefer an APR of 8% with monthly compounding or an APR of 8.5% with semiannual compounding?

8.5% with semiannual compounding

A car dealer offers payments of $522.59 per month for 48 months on a $25,000 car after making a $4,000 down payment. What is the loan's APR?

9%

What is the effective annual interest rate on a 9% APR automobile loan that has monthly payments?

9.38%

A furniture store is offering free credit on purchases over $1,000. You observe that a big-screen television can be purchased for nothing down and $4,000 due in one year. The store next door offers an identical television for $3,650 but does not offer credit terms. Which statement below best describes the cost of the "free" credit?

9.59%

You are considering the purchase of a home that would require a mortgage of $150,000. How much more in total interest will you pay if you select a 30-year mortgage at 5.56% rather than a 15-year mortgage at 4.9%

99.595.80

How many monthly payments remain to be paid on an 8% mortgage with a 30-year amortization and monthly payments of $733.76, when the balance reaches one-half of the $100,000 mortgage?

Approximately 91 payments

Given a set future value, which of the following will contribute to a lower present value?

Higher discount rate

A cash-strapped young professional offers to buy your car with four, equal annual payments of $3,000, beginning 2 years from today. Assuming you're indifferent to cash versus credit, that you can invest at 10%, and that you want to receive $9,000 for the car, should you accept?

No; present value is $8,645.09

Which one of the following factors is fixed and thus cannot change for a specific perpetuity?

Payment amount

What is the relationship between an annually compounded rate and the annual percentage rate (APR) which is calculated for truth-in-lending laws for a loan requiring monthly payments?

The APR is lower than the annually compounded rate.

What happens over time to the real cost of purchasing a home if the mortgage payments are fixed in nominal terms an inflation is in existence?

The real cost is decreasing

Under which of the following conditions will a future value calculated with simple interest exceed a future value calculated with compound interest at the same rate?

This is not possible with positive interest rates.

A stream of equal cash payments lasting forever is termed:

a perpetuity

If interest is paid m times per year, then the per-period interest rate equals the:

annual percentage rate divided by m

Real interest rates:

can be negative, zero, or positive

The APR on a loan must be equal to the effective annual rate when:

compounding occurs annually

Which one of the following will increase the present value of an annuity, other things equal?

decreasing the interest rate

The present value of a perpetuity can be determined by:

dividing the payment by the interest rate

An interest rate has been annualized using compound interest is termed the:

effective annual interest rate

Other things being equal, the more frequent the compounding period the:

higher the effective annual interest rate

Assume you are making $989 monthly payments on your amortized mortgage. The amount of each payment that is applied to the principal balance:

increase with each succeeding payment

Assume your uncle recorded his salary history during a 40-year career and found that it had increased 10-fold. If inflation averaged 4% annually during the period, then over his career his purchasing power:

increased by nearly 2% annualy

When an investment pays only simple interest, this means:

interest is earned only on the original investment

The concept of compound interest refers to:

payment of interest on previously earned interest

Cash flows occurring is different periods should not be compared unless:

the flows have been discounted to a common date

An amortizing loan is one in which:

the principal balance is reduced with each payment.