Francis Peabody just won the $89,000,000 California State Lottery. The lottery offers the winner a choice of receiving

Francis Peabody just won the $89,000,000 California State Lottery. The lottery offers the winner a choice of receiving the winnings in a lump sum or in 26 equal annual installments to be made at the beginning of each year. Assume that funds would be invested at 7.65%. Francis is trying to decide whether to take the lump sum or the annual installments. What is the amount of the lump sum that would be exactly equal to the present value of the annual installments? Round off to the nearest $1.

A) $89,000,000

B) $38,163,612

C) $13,092,576

D) $41,083,128

When comparing annuity due to ordinary annuities, annuity due annuities will have higher

A) present values.

B) annuity payments.

C) future values.

D) both A and C.

E) all of the above.

Gina Dare, who wants to be a millionaire, plans to retire at the end of 40 years. Gina's plan is to invest her money by depositing into an IRA at the end of every year. What is the amount that she needs to deposit annually in order to accumulate $1,000,000? Assume that the account will earn an annual rate of 11.5%. Round off to the nearest $1.

A) $1,497

B) $5,281

C) $75

D) $3,622

As time increases for an amortized loan, the ________ decreases.

A) interest paid per payment

B) principal paid per payment

C) the outstanding loan balance

D) both A and C

Answer:  D

A commercial bank will loan you $7,500 for two years to buy a car. The loan must be repaid in 24 equal monthly payments

A commercial bank will loan you $7,500 for two years to buy a car. The loan must be repaid in 24 equal monthly payments. The annual interest rate on the loan is 12% of the unpaid balance. What is the amount of the monthly payments?

A) $282.43

B) $390.52

C) $369.82

D) $353.05

You wish to borrow $2,000 to be repaid in 12 monthly installments of $189.12. The annual interest rate is

A) 24%.

B) 8%.

C) 18%.

D) 12%.

If you have $20,000 in an account earning 8% annually, what constant amount could you withdraw each year and have nothing remaining at the end of five years?

A) $3,525.62

B) $5,008.76

C) $3,408.88

D) $2,465.78

If you invest $750 every six months at 8% compounded semi-annually, how much would you accumulate at the end of 10 years?

A) $10,065

B) $10,193

C) $22,334

D) $21,731

Your company has received a $50,000 loan from an industrial finance company. The annual payments are $6,202.70. If the company is paying 9% interest per year, how many loan payments must the company make?

A) 15

B) 13

C) 12

D) 19

 ________ annuities involve depositing money at the end of the period and allowing it to grow.

A) Discount

B) Compound

C) Annuity due

D) Both B and C

What is the annual compounded interest rate of an investment with a stated interest rate of 6% compounded quarterly

What is the annual compounded interest rate of an investment with a stated interest rate of 6% compounded quarterly for seven years (round to the nearest .1%)?

A) 51.7%

B) 6.7%

C) 10.9%

D) 6.1%

Which of the following provides the greatest annual interest?

A) 10% compounded annually

B) 9.5% compounded monthly

C) 9% compounded quarterly

D) 8.5% compounded daily

The effective annual rate increases when the ________ increases.

A) number of compounding periods in a year

B) number of years invested

C) quoted rate

D) both A and C

E) all of the above

You are considering two investments. Investment A yields 10% compounded quarterly. Investment B yields r% compounded semiannually. Both investments have equal annual yields. Find r.

A) 19.875%

B) 10%

C) 10.38%

D) 10.125%

The annual percentage rate (APR) is calculated as which of the following?

A) Interest rate per period x compounding periods per year

B) (1+quoted annual rate/compounding periods per year)compounding periods per year-1

C) Interest rate per period / compounding periods per year

D) 1+quoted annual rate/compounding periods per year)1/compounding periods per year-1

For any number of compounding periods per year greater than 1, EAR will always be greater than the APR.

Answer:  TRUE

As the number of compounding periods per year increase, the annual percentage rate of interest increases.

Answer:  FALSE

A monthly credit card interest rate of 1.5% is equal to and effective annual rate of 19.56%

Answer:  TRUE

The annual percentage rate on two different investments will equal the effective annual rate on the two investments only if interest on both investments is compounded annually.

Answer:  TRUE

California Investors recently advertised the following claim: Invest your money with us at 21%, compounded annually

California Investors recently advertised the following claim: Invest your money with us at 21%, compounded annually, and we guarantee to double your money sooner than you imagine. Ignoring taxes, how long would it take to double your money at a nominal rate of 21%, compounded annually? Round off to the nearest year.

A) Approximately two years

B) Approximately four years

C) Approximately six years

D) Approximately eight years

Using a financial calculator, which of the following would be a correct way to find how long it would take for a sum to triple at a rate of 3%?

A) i=5, PV=-1, PMT = 0, FV=3, solve for N

B) i=5, PV=1, PMT = 0, FV=3, solve for N

C) i=.05, PV=-1, PMT = 0, FV=3, solve for N

D) Financial calculators cannot be used to solve this problem.

Stephen's grandmother deposited $100 in an investment account for him when he was born, 25 years ago. The account is now worth $1,500.  What was the average rate of return on the account?

A) 6.00%

B) 16.67%

C) 15.00%

D) 11.44%

Stephen's grandmother deposited $100 in an investment account for him when he was born, 25 years ago. The account is now worth $1,500.  What was the average rate of return on the account?  Which of the following is a correct way to solve this problem using EXCEL?

A) =PV(25,i,-100,1500)

B) =rate(25,0,100,1500)

C) =rate(25,0,-100,1500)

D) =rate(0,-100,1500,25)

The present value of $400 to be received at the end of 10 years, if the discount rate is 5%, is

A) $400.00.

B) $248.40.

C) $313.60.

D) $245.60.

The present value of $1,000 to be received at the end of five years, if the discount rate is 10%, is

A) $621.

B) $784.

C) $614.

D) $500.

What is the present value of an investment that pays $400 at the end of three years and $700 at the end of 10 years if the discount rate is 5%?

A) $1,100.00

B) $675.30

C) $775.40

D) $424.60

The present value of a single sum

A) increases as the discount rate decreases.

B) decreases as the discount rate decreases.

C) increases as the number of discount periods increases.

D) increases as the discount rate increases.

E) none of the above.

As the discount rate increases, the present value of future cash flows increases.

Answer:  FALSE

As the compound interest rate increases, the present value of future cash flows decreases.

Answer:  TRUE

The present value of a future sum of money increases as the number of years before the payment is received increases.

Answer:  FALSE

When calculating either discount rates or the number of periods using a financial calculator, the PV and FV must have opposite signs.

Answer:  TRUE

Three years from now, Barbara Waters will purchase a laptop computer that will cost $2,250. Assume that Barbara

Three years from now, Barbara Waters will purchase a laptop computer that will cost $2,250. Assume that Barbara can earn 6.25% (compounded monthly) on her money. How much should she set aside today for the purchase? Round off to the nearest $1.

A) $1,250

B) $900

C) $1,866

D) $3,775

If you want to have $875 in 32 months, how much money must you put in a savings account today? Assume that the savings account pays 16% and it is compounded monthly (round to the nearest $10).

A) $630

B) $570

C) $650

D) $660

Which of the following is the formula for present value?

A) FVn = P(1 + i)n 

B) FVn = (1 + i)/P

C) FVn = P/(1 + i)n 

D) FVn = P(1 + i)-n 

All else constant, the present value of an investment will increase if

A) the investment is discounted at a higher interest rate. 

B) the investment is discounted for fewer years.

C) the investment is discounted at a lower interest rate.

D) both B and C.

Answer:  D

To find the present value of $1000 discounted for 20 years at 8%, when using a financial calculator, the correct entry is

A) N=20, i=.08,PMT = 0, FV=1000 solve for PV

B) N=20, i=8,PMT = 0, FV=1000 solve for PMT

C) N=20, i=.08,PMT = 0, PV=1000 solve for FV

D) N=20, i=8,PMT = 0, FV=1000 solve for PV

What is the present value of $1,000 to be received 10 years from today? Assume that the investment pays 8.5%

What is the present value of $1,000 to be received 10 years from today? Assume that the investment pays 8.5% and it is compounded monthly (round to the nearest $1).

A) $893

B) $3,106

C) $429

D) $833

The present value of a single future sum

A) increases as the number of discount periods increases.

B) is generally larger than the future sum.

C) depends upon the number of discount periods.

D) increases as the discount rate increases.

Assuming two investments have equal lives, a high discount rate tends to favor

A) the investment with large cash flow early.

B) the investment with large cash flow late.

C) the investment with even cash flow.

D) neither investment since they have equal lives.

High discount rates favor

A) neither long-term nor short-term investments.

B) both long-term and short-term investments.

C) long-term investments.

D) short-term investments.

An increase in ________ will decrease present value.

A) the discount rate per period

B) the original amount invested

C) the number of periods

D) both A and C

What is the present value of $12,500 to be received 10 years from today? Assume a discount rate of 8% compounded annually and round to the nearest $10.

A) $5,790

B) $11,574

C) $9,210

D) $17,010

Your bank has agreed to loan you $3,000 if you agree to pay a lump sum of $5,775 in five years.

Your bank has agreed to loan you $3,000 if you agree to pay a lump sum of $5,775 in five years. What annual rate of interest will you be paying?

Answer:  FVIF[? %, 5 yr] $3,000 = $5,775

FVIF[? %, 5 yr] = $1.925

i = 14%

 Briefly discuss how non-annual compounding (more than one compounding period per year) is preferable to annual compounding if you are an investor.

Answer:  Non-annual compounding is preferable to annual compounding because with non-annual compounding, interest is compounded more frequently within a year period. This means that more interest on interest would be generated on a given investment.

If you deposit $1,000 each year in a savings account earning 4%, compounded annually, how much will you have in 10 years?

Answer:  FV[10] = $1,000(12.006) = $12,006

Earnings per share for XYZ, Inc. grew constantly from $7.99 in 1974 to $12.68 in 1980. What was the compound annual growth rate in earnings-per-share over the period?

Answer:  $12.68 = $7.99 FVIF[? %, 6 yr]

1.587 = FVIF[? %, 6 yr]

        g = 8%

If you invest $450 today and it increases to $6,185 at the end of 20 years, what rate of return have you earned?

Answer:  $6,185 = $450 FVIF[? %, 20 yr]

13.743 = FVIF[? %, 20 yr]

i = 14%