Question 1

Which of the following statements regarding a 15-year (180-month)$125,000,fixed-rate mortgage is CORRECT? (Ignore taxes and transactions costs. )

Accepted Answer

A)  The remaining balance after three years will be $125,000 less one third of the interest paid during the first three years. 
B)  Because it is a fixed-rate mortgage,the monthly loan payments (which include both interest and principal payments)are constant. 
C)  Interest payments on the mortgage will increase steadily over time,but the total amount of each payment will remain constant. 
D)  The proportion of the monthly payment that goes towards repayment of principal will be lower 10 years from now than it will be the first year. 
E)  The outstanding balance declines at a slower rate in the later years of the loan's life.

Question 2

Your grandmother just died and left you $47,500 in a trust fund that pays 6.5% interest.You must spend the money on your college education,and you must withdraw the money in 4 equal installments,beginning immediately.How much could you withdraw today and at the beginning of each of the next 3 years and end up with zero in the account?

Accepted Answer

A)  $14,321.05 
B)  $10,415.31 
C)  $12,628.56 
D)  $9,894.54 
E)  $13,019.14

Question 3

Pace Co.borrowed $10,000 at a rate of 7.25%,simple interest,with interest paid at the end of each month.The bank uses a 360-day year.How much interest would Pace have to pay in a 30-day month?

Accepted Answer

A)  $57.40 
B)  $47.13 
C)  $60.42 
D)  $73.10 
E)  $50.15

Question 4

The payment made each period on an amortized loan is constant,and it consists of some interest and some principal.The closer we are to the end of the loan's life,the greater the percentage of the payment that will be a repayment of principal.

Accepted Answer

A) True 
 B)False

Question 5

Your aunt is about to retire,and she wants to sell some of her stock and buy an annuity that will provide her with income of $95,000 per year for 30 years,beginning a year from today.The going rate on such annuities is 7.25%.How much would it cost her to buy such an annuity today?

Accepted Answer

A)  $931,376.84 
B)  $1,172,844.91 
C)  $1,333,823.63 
D)  $1,149,847.96 
E)  $1,241,835.79

Question 6

You want to quit your job and return to school for an MBA degree 3 years from now,and you plan to save $5,000 per year,beginning immediately.You will make 3 deposits in an account that pays 5.2% interest.Under these assumptions,how much will you have 3 years from today?

Accepted Answer

A)  $16,614.78 
B)  $17,943.97 
C)  $17,445.52 
D)  $18,442.41 
E)  $14,953.30

Question 7

After graduation,you plan to work for Dynamo Corporation for 12 years and then start your own business.You expect to save and deposit $7,500 a year for the first 6 years (t = 1 through t = 6)and $15,000 annually for the following 6 years (t = 7 through t = 12).The first deposit will be made a year from today.In addition,your grandfather just gave you a $32,500 graduation gift which you will deposit immediately (t = 0).If the account earns 9% compounded annually,how much will you have when you start your business 12 years from now?

Accepted Answer

A)  $269,003 
B)  $292,914 
C)  $298,892 
D)  $286,936 
E)  $310,848

Question 8

Your company has just taken out a 1-year installment loan for $72,500 at a nominal rate of 20.0% but with equal end-of-month payments.What percentage of the 2nd monthly payment will go toward the repayment of principal?

Accepted Answer

A)  101.72% 
B)  71.70% 
C)  86.71% 
D)  83.37% 
E)  97.55%

Question 9

You have a chance to buy an annuity that pays $2,450 at the beginning of each year for 3 years.You could earn 5.5% on your money in other investments with equal risk.What is the most you should pay for the annuity?

Accepted Answer

A)  $6,973.48 
B)  $7,531.36 
C)  $6,903.75 
D)  $8,298.45 
E)  $8,228.71

Question 10

What annual payment must you receive in order to earn a 6.5% rate of return on a perpetuity that has a cost of $4,800?

Accepted Answer

A)  $352.56 
B)  $255.84 
C)  $349.44 
D)  $283.92 
E)  $312.00

Question 11

Starting to invest early for retirement increases the benefits of compound interest.

Accepted Answer

A) True 
 B)False

Question 12

You sold a car and accepted a note with the following cash flow stream as your payment.What was the effective price you received for the car assuming an interest rate of 5.5%? $$\begin{array} { c c c c c c } 
& 0 & 1 & 2 & 3 & 4 \
\hline\text { CFs: } & \$ 0 & \$ 1,000 & \$ 2,000 & \$ 2,000 & \$ 2,000
\end{array}$$
?

Accepted Answer

A)  $6,123 
B)  $6,062 
C)  $5,335 
D)  $5,214 
E)  $5,699

Question 13

Which of the following statements regarding a 15-year (180-month)$125,000,fixed-rate mortgage is CORRECT? (Ignore taxes and transactions costs. )

Accepted Answer

A)  The remaining balance after three years will be $125,000 less one third of the interest paid during the first three years. 
B)  Because the outstanding balance declines over time,the monthly payments will also decline over time. 
C)  Interest payments on the mortgage will increase steadily over time,but the total amount of each payment will remain constant. 
D)  The proportion of the monthly payment that goes towards repayment of principal will be lower 10 years from now than it will be the first year. 
E)  The outstanding balance declines at a faster rate in the later years of the loan's life.

Question 14

If a bank compounds savings accounts quarterly,the nominal rate will exceed the effective annual rate.

Accepted Answer

A) True 
 B)False

Question 15

What is the present value of the following cash flow stream at a rate of 15.0%? $$\begin{array} { l c c c c c } 
\text { Years: } & 0 & 1 & 2 & 3 & 4 \
\hline \text { CFs: } & \$ 0 & \$ 1,500 & \$ 3,000 & \$ 4,500 & \$ 6,000
\end{array}$$
?

Accepted Answer

A)  $10,859 
B)  $10,261 
C)  $12,453 
D)  $9,962 
E)  $12,154

Question 16

A U.S.Treasury bond will pay a lump sum of $1,000 exactly 3 years from today.The nominal interest rate is 6%,semiannual compounding.Which of the following statements is CORRECT?

Accepted Answer

A)  The periodic interest rate is greater than 3%. 
B)  The periodic rate is less than 3%. 
C)  The present value would be greater if the lump sum were discounted back for more periods. 
D)  The present value of the $1,000 would be larger if interest were compounded monthly rather than semiannually. 
E)  The PV of the $1,000 lump sum has a smaller present value than the PV of a 3-year,$333.33 ordinary annuity.

Question 17

Suppose you inherited $175,000 and invested it at 8.25% per year.How much could you withdraw at the end of each of the next 20 years?

Accepted Answer

A)  $14,888.75 
B)  $18,157.02 
C)  $18,883.30 
D)  $15,070.32 
E)  $21,606.85

Question 18

If we are given a periodic interest rate,say a monthly rate,we can find the nominal annual rate by multiplying the periodic rate by the number of periods per year.

Accepted Answer

A) True 
 B)False

Question 19

As a result of compounding,the effective annual rate on a bank deposit (or a loan)is always equal to or greater than the nominal rate on the deposit (or loan).

Accepted Answer

A) True 
 B)False

Question 20

If the discount (or interest)rate is positive,the present value of an expected series of payments will always exceed the future value of the same series.

Accepted Answer

A) True 
 B)False

Exam 5: Time Value of Money

Which of the following statements regarding a 15-year (180-month) $125,000,fixed-rate mortgage is CORRECT? (Ignore taxes and transactions costs. )

Pace Co.borrowed $10,000 at a rate of 7.25%,simple interest,with interest paid at the end of each month.The bank uses a 360-day year.How much interest would Pace have to pay in a 30-day month?

The payment made each period on an amortized loan is constant,and it consists of some interest and some principal.The closer we are to the end of the loan's life,the greater the percentage of the payment that will be a repayment of principal.

Your aunt is about to retire,and she wants to sell some of her stock and buy an annuity that will provide her with income of $95,000 per year for 30 years,beginning a year from today.The going rate on such annuities is 7.25%.How much would it cost her to buy such an annuity today?

You want to quit your job and return to school for an MBA degree 3 years from now,and you plan to save $5,000 per year,beginning immediately.You will make 3 deposits in an account that pays 5.2% interest.Under these assumptions,how much will you have 3 years from today?

Your company has just taken out a 1-year installment loan for $72,500 at a nominal rate of 20.0% but with equal end-of-month payments.What percentage of the 2nd monthly payment will go toward the repayment of principal?

You have a chance to buy an annuity that pays $2,450 at the beginning of each year for 3 years.You could earn 5.5% on your money in other investments with equal risk.What is the most you should pay for the annuity?

What annual payment must you receive in order to earn a 6.5% rate of return on a perpetuity that has a cost of $4,800?

Starting to invest early for retirement increases the benefits of compound interest.

Which of the following statements regarding a 15-year (180-month) $125,000,fixed-rate mortgage is CORRECT? (Ignore taxes and transactions costs. )

If a bank compounds savings accounts quarterly,the nominal rate will exceed the effective annual rate.

What is the present value of the following cash flow stream at a rate of 15.0%? $\begin{array} { l c c c c c } \text { Years: } & 0 & 1 & 2 & 3 & 4 \\\hline \text { CFs: } & \$ 0 & \$ 1,500 & \$ 3,000 & \$ 4,500 & \$ 6,000\end{array}$ ?

A U.S.Treasury bond will pay a lump sum of $1,000 exactly 3 years from today.The nominal interest rate is 6%,semiannual compounding.Which of the following statements is CORRECT?

Suppose you inherited $175,000 and invested it at 8.25% per year.How much could you withdraw at the end of each of the next 20 years?

If we are given a periodic interest rate,say a monthly rate,we can find the nominal annual rate by multiplying the periodic rate by the number of periods per year.

As a result of compounding,the effective annual rate on a bank deposit (or a loan)is always equal to or greater than the nominal rate on the deposit (or loan).

If the discount (or interest)rate is positive,the present value of an expected series of payments will always exceed the future value of the same series.