Econ 2560 chapter 5 practice questions and answers PDF

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Help | Julia Milone System Homepage [PRINT] ECON*2560 01/02 Theory of Finance W19 Nancy Bower,

Question 1: Score 0/1 Suppose you will receive payments of $9,000 at the beginning of the next 13 years (i.e., the first payment is today). What is the present value of all the payments? The interest rate is 5%. ! Enter your response below (rounded to 2 decimal places). Your response

Correct response 88,769.26±5 Grade: 0/1.0

Total grade: 0.0×1/1 = 0% Feedback: An annuity due is a level stream of cash flows starting immediately. The formula for the present value of an annuity due is given by PV 9,000, the interest rate is r = 0.05, and!t

= c+c

1 − 1 !where the payments are c = (r r(1+r ) (t−1) )

= 13.

! Substituting the values into the formula above will give the answer $88769.26.

Question 2: Score 0/1 Suppose a condo generates $17,000 in cash flows in the first year. If the cash flows grow at 1% per year, the interest rate is 7%, and the building will be sold at the end of 20 years with a value of $70,000, what is the present value of the condo's cash flow? ! Enter your response below (rounded to 2 decimal places).

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Your response

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Correct response 212,081.91±100 Grade: 0/1.0

Total grade: 0.0×1/1 = 0% Feedback: The formula for the present value of a growing annuity with a final payment is

1+g t v c PV = + r− g 1− ( 1+r ) ) . The first part of the equation is the present value of ( (1+r) t v the final payment, . The second part of the equation is the formula for a growing annuity, (1+r) t ! (1+g ) t c − r−g (1 ( (1+r) ) ) .!! ! The variables to substitute into the equation are the final payment! v = 70,000, the annual payments !c = !17,000, the interest rate ! r = !0.07, t = 20!, and the growth rate ! g = !0.01.! ! Substituting the values into the equation gives the answer $212081.91.

Question 3: Score 0/1 If you deposit $1,000 into a bank account today, what annually compounded interest rate would you need to earn in order to have $2,100 in 11 years? Enter your answer as a percentage rounded!2 decimal places. !Do not enter the % sign. ! Enter your answer below. Your response

Correct response 6.98±0.03 Grade: 0/1.0

%

Total grade: 0.0×1/1 = 0% Feedback:

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The formula for the future value of a single cash flow is FV = PV(1+r)t . !In this example, the future value is FV = $2,100, the present value is PV = $1,000, and the time is 11 years. !Solving, you get that!the interest rate that you would need to earn in order to have $1,000 in 11 years is!(2,100/1,000) (1/11)! - 1 = 6.98% ! !

Question 4: Score 0/1 Suppose you take out a car loan that requires you to pay $7,000 now, $3,000 at the end of year 1, and $6,000 at the end of year 2. The interest rate is 5% now and increases to 6% in the next year. What is the present value of the payments?

! Enter your response below rounded to 2 decimal places. Your response

Correct response 15,247.98±5 Grade: 0/1.0

Total grade: 0.0×1/1 = 0% Feedback: The present value formula is given by!PV

c1 c2 = c0 + + 1+r 1 (1+ r1 )( 1+r 2)

where !ci !refers

to the cash flow at time i !and r i !refers to the interest rate during period i. Because the interest rate is different in the two periods, the time 2 cash flow is discounted back to time 1 using r 2 !(6%) and discounted back to today using r 1 !(5%). ! The formula is constructed as follows. The first payment occurs now. Therefore, the first payment,! c0 , is $7,000. Since the payment occurs now, the value does not need to be discounted. ! The payments are than 3,000 next year and 6,000 in the second year. Therefore the next 2 payments are given by!c1 = 3,000 and c 2 = !6,000. ! The interest rate does not change until after the first year. Therefore, the first payment is only discounted by the first interest rate r 1 = !0.05. 3 of 7

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! The interest rate then changes to 6% in year two. The second payment of 6,000 must first be discounted by the interest rate 6% in year two. Then in year one, the interest rate was 5%. Therefore, we discount the second payment by 0.05 in the first year. This gives the denominator! (1

+ r 1 ) (1 + r 2 ) .

! Substitutiing the values into the equation will give the answer $15,247.98.

Question 5: Score 0/1 If you invest $8,000 into a savings account at 3% interest per year (APR), compounded monthly, how much will you have in the savings account after 19 years? ! Enter your response below (rounded to 2 decimal places). Your response

Correct response 14,136.08±1 Grade: 0/1.0

!

Total grade: 0.0×1/1 = 0% Feedback: The equation to calculate the total value at the end of year 19 is given by

(12 t) where!PV = 8,000, r = 0.03, and t = 19. To calculate future value FV = PV ( 1 + 1 r ) 12 when there is monthly compound interest, the interest rate must be divided by 12 and the number of periods is multiplied by 12. Substituting the values into the equation gives the answer $14,136.08. ! !

Question 6: Score 0/1 If you invest $3,000 into a savings account at an annual interest rate of 3% (APR), compounded semiannually, how much will you have in the savings account after 18 years?

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! Enter your response below (rounded to 2 decimal places). Your response

Correct response 5,127.42±5 Grade: 0/1.0

! !

Total grade: 0.0×1/1 = 0% Feedback: The equation to calculate the total value at the end of year 18 is given by

(2t) FV = PV (1 + 1 r) 2

where!PV = 3,000, r = 0.03, and t = 18. To calculate future value when there is semi-annual compound interest, the interest rate must be divided by 2 and the number of periods is multiplied by 2. Substituting the values into the equation gives the answer $5,127.42. ! !

Question 7: Score 0/1 An investment will pay you $18,200 in 11 years. The stated interest rate is 12% (APR). If interest is compounded continuously, what is the present value? ! Enter your response below rounded to two decimal places. Your response

Correct response 4,861.86±5 Grade: 0/1.0

Total grade: 0.0×1/1 = 0% Feedback: The formula for the present value is!PV = FVe − rt where! FV = 18,200,!r = 0.12, and!t = 11. Substituting the values into the equation gives the answer $4,861.86. (The value for e is 2.718282.)

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Question 8: Score 0/1 An investment promises to pay you $5,500 per year starting in 5 years. The cash flow from the investment is expected to increase by 3% per year forever. If alternative investments of similar risk earn a return of 7% per year, determine the maximum you would be willing to pay for this investment today. ! Enter your response below (rounded to 2 decimal places). Your response

Correct response 104,898.09±10 Grade: 0/1.0

Total grade: 0.0×1/1 = 0% Feedback: The present value of the payment at time t-1 is given by! PV t−1 is!r = 0.07, the growth rate! g = 0.03, and the payment is!c formula gives an answer of 137,500.

= r−cg

where the interest rate

= 5,500. Substituting the values into the

!

PVt−1 (1 +r ) t −1 answer $104,898.09. (The value of!PV t −1 = !137,500) PV 0 =

The formula for the present value is!

! where

t=

5.!Substituting the values into the formulas gives the

Question 9: Score 0/1 Suppose you deposit $7,000 into your bank account at the end of each of the next 9 years. If the interest rate is 6%, how much would you have accumulated at the end of 9 years? ! Enter your response below (rounded to 2 decimal places). Your response

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Correct response 80,439.21±10 Grade: 0/1.0

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Total grade: 0.0×1/1 = 0% Feedback: The formula for the future value of a stream of constant cash flows is given by

FV = c

t ( (1+r) −1) !where the payments are c= r ( )

7,000, the interest rate is r = 0.06, and t = 9

! Substituting the values into the formula gives the answer $80439.21.

Question 10: Score 0/1 An investment promises to pay you $9,000 per year forever with the first payment at time 1. If alternative investments of similar risk earn 7.45% per year, determine the maximum you would be willing to pay for this investment. ! Enter your response below (rounded to 2 decimal places). Your response No answer

Correct response 120805.37 Grade: 0/1.0

Total grade: 0.0×1/1 = 0% Feedback: The formula for the present value of a perpetuity when payments occur at the end of the period is given by, !

PV = cr ! where the payments are c = 9,000 and the interest rate is r =0.0745. Substituting the values into the equation above gives the answer $120805.37.

! Build Number : 1268638

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