Quiz 3 Finance (chapter 5-6)

You invested $6,500 at 6 percent simple interest. How much more could you have earned over a 10-year period if the interest had compounded annually?

$1,240.51 FVSimple = $6,500 + ($6,500)(.06)(10) FVSimple = $10,400FV Compound = $6,500(1.06''10) FVCompound = $11,640.51 Difference = $11,640.51 − 10,400Difference = $1,240.51

All else constant, which one of the following will result in the lowest present value of a lump sum?

8 percent interest for 10 years

Your credit card charges you .85 percent interest per month. This rate when multiplied by 12 is called the ____ rate.

annual percentage

The interest rate that is most commonly quoted by a lender is referred to as the:

annual percentage rate.

The interest earned on both the initial principal and the interest reinvested from prior periods is called:

compound interest.

Madelyn is calculating the present value of a bonus she will receive next year. The process she is using is called:

discounting.

A preferred stock pays an annual dividend of $5.20. What is one share of this stock worth today if the rate of return is 10.44 percent?

PV = $5.20/.1044 PV = $49.81

The variable that you are solving for in a present value of a lump sum problem is:

Present value

The variable that you are solving for in a present value of an annuity problem is:

The Present value

What is the present value of $1,000 to be received in 12 years invested at a rate of 8%?

N = 12 I/YR = 8 PMT = $0 FV = $1,000 PV = ??? = $397

What is the future value of $400 invested each year for 15 years at a rate of 6%?

N = 15 I/YR = 6 PV = $0 PMT = $400 FV = ??? = $9,310

What is the present value of $1,200 to be received in 18 years invested at a rate of 5%?

N = 18 I/YR = 5 PMT = $0 FV = $1,200 PV= ??? = $499

The variables in a future value of an annuity problem include all of the following, except:

Usage

The variables in a present value of an annuity problem include all of the following, except:

Risk Profile

Assume the total cost of a college education will be $245,000 when your child enters college in 15 years. You presently have $108,000 to invest for this purpose. What annually compounded rate of interest must you earn to cover the cost of your child's college education?

$245,000 = $108,000[(1 + r)15] r = .0561, or 5.61%

A perpetuity is defined as:

unending equal payments paid at equal time intervals.

Your credit card company charges you 1.15 percent interest per month. What is the APR?

APR = .0115(12) APR = .1380, or 13.80%

Which one of the following statements concerning interest rates is correct?

The effective annual rate equals the annual percentage rate when interest is compounded annually.

Jonathan invested $6,220 in an account that pays 11 percent simple interest. How much money will he have at the end of 40 years?

$33,588 FV = $6,220 + ($6,220)(.11)(40)

Finn intends to save $2,000 per year, and expects to earn an annual rate of 6.9 percent. How much will he have in his account at the end of 37 years?

FVA = $2,000[(1.069''37 − 1)/.069] FVA = $313,274.38

How would a decrease in the interest rate effect the present value of a lump sum, single amount problem (all other variables remain the same)?

Increase the present value.

A common error made when solving a future value of an annuity problem is:

Multiplying the annual deposit and the number of years before calculating the problem.

The variables in a future value of a lump sum problem include all of the following, except:

Volatility

The variables in a future value of an annuity problem include all of the following, except:

Volatility

What is the future value in 60 years of $7,440 invested today at 9 percent interest, compounded annually? Multiple Choice

$1,309,673 FV = $7,440(1 + .0960) FV = $1,309,673

What is the future value of $1,000 invested for 15 years at a rate of 5%?

$2,079 N = 15 I/YR = 5 PV = $1,000 PMT = $0

What is the future value of $1,000 invested for 15 years at a rate of 5%?

$2,079 N = 15 I/YR = 5 PV = $1,000 PMT = $0 FV = ??? = $2,079

You are paying an EAR of 16.78 percent on your credit card. The interest is compounded monthly. What is the annual percentage rate on this account?

APR = 12(1.1678''1/''12 − 1) APR = .1561, or 15.61%

What is the future value of $500 invested each year for 20 years at a rate of 10%?

$28,637 N = 20 I/YR = 10 PV = $0 PMT = $500 FV = ??? = $28,637

Assume you intend to retire 47 years from today. Your current salary is $80,000 per year, and you expect to earn salary increases of 3.25 percent each year. What annual salary do you expect to earn 47 years from today?

$359,685 FV = $80,000(1.0325 ''47) FV = $359,685

What is the present value of $1,000 to be received in 12 years invested at a rate of 8%?

$397 N = 12 I/YR = 8 PMT = $0 FV = $1,000 PV = ??? = $397

How would a decrease in the interest rate effect the future value of a lump sum, single amount problem (all other variables remain the same)?

Decrease the future value.

How would an increase in the interest rate effect the present value of an annuity problem (all other variables remain the same)?

Decrease the present value.

You are considering two savings options. Both options offer a rate of return of 8.3 percent. The first option is to save $1,500, $1,250, and $6,400 at the end of each year for the next three years, respectively. The other option is to save one lump sum amount today. You want to have the same balance in your savings account at the end of the three years, regardless of the savings method you select. If you select the lump sum method, how much do you need to save today?

PV = $1,500/1.083 + $1,250/1.0832 + $6,400/1.0833 PV = $7,489

Suppose the first comic book of a classic series was sold in 1954. In 2020, the estimated price for this comic book was $310,000, which is an annually compounded return of 22 percent. For this to be true, what was the original price of the comic book in 1954?

PV = $310,000/1.2266 PV = $.62

Andrew just calculated the present value of a $15,000 bonus he will receive next year. The interest rate he used in his calculation is referred to as the:

discount rate.

The process of determining the present value of future cash flows in order to know their value today is referred to as:

discounted cash flow valuation.

The actual interest rate on a loan that is compounded monthly but expressed as an annual rate is referred to as the _____ rate.

effective annual

You just paid $480,000 for an annuity that will pay you and your heirs $15,000 a year forever. What rate of return are you earning on this policy?

r = $15,000/$480,000 r = .03125, or 3.125%

Claire's coin collection contains fifty 1948 silver dollars. Her grandparents purchased them at their face value in 1948. These coins have appreciated by 7.6 percent annually. How much is the collection expected to be worth in 2025?

$14,077.16 FV = $50(1.07677)

On your tenth birthday, you received $300 which you invested at 4.5 percent interest, compounded annually. Your investment is now worth $756. How old are you today?

Age 31 $756 = $300(1.045t) t = 21 years Age today = 10 + 21 Age today = 31 years

The variables in a future value of a lump sum problem include all of the following, except:

Annuity Payments

What is the EAR if a bank charges you an APR of 7.65 percent compounded quarterly?

EAR = (1 + .0765/4)''4 − 1 EAR = .0787, or 7.87%

Javier and Alex plan on retiring 27 years from today. At that time, they plan to have saved the same amount. Javier is depositing $15,000 today at an annual interest rate of 5.2 percent. How will Alex's deposit amount vary from Javier's if Alex also makes a deposit today, but earns an annual interest rate of 6.2 percent? Alex's deposit will need to be ______ than Javier's. (Assume annual compounding on both accounts.) Multiple Choice

FV = $15,000(1.05227) FV = $58,954.40 PV = $58,954.40/1.06227 PV = $11,618.61 Difference = $11,618.61 − 15,000 Difference = −$3,381.39

What is the present value of $500 invested each year for 10 years at a rate of 5%?

N = 10 I/YR = 5 PMT = $500 FV = $0 PV = ??? = 3,861

What is the present value of $400 invested each year for 12 years at a rate of 6%?

N = 12 I/YR = 6 PMT = $400 FV = $0 PV = ??? = $3,354

What is the future value of $500 invested each year for 20 years at a rate of 10%?

N = 20 I/YR = 10 PV = $0 PMT = $500 FV = ??? = $28,637

Which one of the following variables is the exponent in the present value formula?

Number of time periods

Your bank pays 1.2 percent compounded daily on its savings accounts. If you deposit $7,500 today, how much will you have in your account 15 years from now?

FV = $7,500[1 +(.012/365)]'(15)'(365) FV = $8,979.10

The variables in a present value of a lump sum problem include all of the following, except:

Free Cash Flow

The variable that you are solving for in a future value of an annuity problem is:

Future value

You have just received notification that you have won the $1.25 million first prize in the Centennial Lottery. The prize will be awarded on your 100th birthday, 79 years from now. The appropriate discount rate is 6.4 percent, compounded annually. What is the present value of your winnings?

PV = $1,250,000/(1.06479) PV = $9,300.82

The variables in a present value of an annuity problem include all of the following, except:

Source of funds

Assume your mother invested a lump sum 28 years ago at 4.05 percent interest, compounded annually. Today, she gave you the proceeds of that investment, totaling $48,613.24. How much did your mother originally invest?

PV = $48,613.24/1.0405''28PV = $15,994.70

Sara wants to establish a trust fund to provide $75,000 in scholarships each year. She believes the fund can earn a fixed 6.15 percent annual rate of return. How much money must she contribute to establish the fund?

PV = $75,000/.0615PV = $1,219,512

The variables in a future value of a lump sum problem include all of the following, except:

Payments

The variables in a present value of a lump sum problem include all of the following, except:

Payments

Which one of the following statements related to loan interest rates is correct?

When comparing loans you should compare the effective annual rates.