My Courses / FIN035005-U18E / Lecture 3 / HW3
Started on Monday, June 18, 2018, 10:28 PM
State Finished
Completed on Monday, June 18, 2018, 10:30 PM
Time taken 1 min 55 secs
Points 16/16
Grade 100 out of 100
Question 1
Correct
1.00 points out of 1.00
You have just taken out a five-year loan from a bank to buy an engagement ring. The ring costs $5,000. You
plan to put down $2,000 and borrow $3,000. You will need to make annual payments of $1,100 at the end of
each year. Show the timeline of the loan from your perspective.
Select one:
A.
Year
0
1
2
3
4
5
------------------|-------------|-------------|-------------|-------------|------------|
Cash Flow -$3000 $1100
$1100
$1100
$1100
$1100
B.
Year
0
1
2
3
4
5
------------------|-------------|-------------|-------------|-------------|------------|
Cash Flow
-$2000
$1100
$1100
$1100
$1100
$1100
C.
Year
0
1
2
3
4
5
------------------|-------------|-------------|-------------|-------------|------------|
Cash Flow
$5000
-$1100
-$1100
-$1100
-$1100
-$1100
D.
Year
0
1
2
3
4
5
------------------|-------------|-------------|-------------|-------------|------------|
Cash Flow $3000
-$1100
-$1100
-$1100
-$1100
-$1100
Your answer is correct.
Hint: from your perspective on the loan (not the purchase transaction), you received $3,000 today and you will
make 5 installments of $1,100 at the end of each of the next five years.
The correct answer is:
Year
0
1
2
3
4
5
------------------|-------------|-------------|-------------|-------------|------------|
Cash Flow $3000 -$1100 -$1100
-$1100
-$1100
-$1100
Question 2
Correct
1.00 points out of 1.00
You currently have a four-year-old mortgage outstanding on your house. You make monthly payments of
$1,700. You have just made a payment. The mortgage has 26 years to go (i.e., it had an original term of 30
years). Show the timeline of the loan from the bank's perspective.
Select one:
A.
Year:
0
1
2
3
4
360
------------------|-------------|------------|------------|------------|-- - - - - - - - - --|
Cash Flow: $1700 $1700
$1700
$1700 $1700
$1700
B.
Year:
0
1
2
3
4
312
------------------|-------------|------------|------------|------------|-- - - - - - - - - --|
Cash Flow:
$1700 $1700
$1700
$1700
$1700
C.
Year:
0
1
2
3
4
360
------------------|-------------|------------|------------|------------|-- - - - - - - - - --|
Cash Flow: -$1700 -$1700 -$1700 -$1700 -$1700
-$1700
D.
Year:
0
1
2
3
4
312
------------------|-------------|------------|------------|------------|-- - - - - - - - - --|
Cash Flow:
-$1700 -$1700 -$1700 -$1700
-$1700
Your answer is correct.
Hint: Since you have just made a monthly payment, you do not have any payment due TODAY and the next
payment is due at the end of the month.
The correct answer is:
Year:
0
1
2
3
4
312
------------------|-------------|------------|------------|------------|-- - - - - - - - - --|
Cash Flow:
$1700
$1700
$1700
$1700
$1700
Question 3
Correct
1.00 points out of 1.00
Calculate the future value of $2,000 in:
(a) 5 years at an interest rate of 8% per year. $ 2939
. (Round to the nearest dollar.)
(b) 10 years at an interest rate of 8% per year. $ 4318
. (Round to the nearest dollar.)
(c) 5 years at an interest rate of 16% per year. $ 4201
. (Round to the nearest dollar.)
(d) Why is the amount of interest earned in part (a) less than half the amount of interest earned in part (b)?
The amount of interest earned in part (a) is really half of the amount of interest earned in part (b) since in
part (b) the money grows for twice as many years as in part (a).
The annual interest rate in part (b) is slightly higher than the rate assumed in part (a).
The interest rate earned in part (a) is based on a lower effective annual interest rate.
This results because you earn interest on past interest. Since more interest has been paid at the end of
time period than at the beginning, the money grows faster.
1.00 points out of 1.00
The correct answer is: This results because you earn interest on past interest. Since more interest has
been paid at the end of time period than at the beginning, the money grows faster.
Hint: FV = PV × (1+r)n
(a) $2,000 * (1.08)5
(b) $2,000 * (1.08)10
(c) $2,000 * (1.16)5
Question 4
Correct
1.00 points out of 1.00
What is the present value of $14,000 received:
(a) 12 years from today when the interest rate is 4% per year. $ 8744
. (Round to the nearest dollar.)
(b) 20 years from today when the interest rate is 5% per year. $ 5276
. (Round to the nearest dollar.)
(c) 6 years from today when the interest rate is 2% per year. $ 12432
. (Round to the nearest dollar.)
Hint: PV = FV ÷ (1+r)n
(a)$14,000 ÷ (1+4%)12
(b)$14,000 ÷ (1+5%)20
(c)$14,000 ÷ (1+2%)6
Question 5
Correct
1.00 points out of 1.00
Your daughter is currently 6 years old. You anticipate that she will be going to college in 12 years. You would
like to have $144,000 in a savings account to fund her education at that time. If the account promises to pay a
fixed interest rate of 7% per year, how much money do you need to put into the account today to ensure that
you will have $144,000 in 12 years?
Your deposit today should be $ 63938
Hint: PV = FV ÷ (1+r)n
PV = $144,00 ÷ (1+7%)12
. (Round to the nearest dollar.)
Question 6
Correct
1.00 points out of 1.00
You are thinking of retiring. Your retirement plan will pay you either $250,000 immediately on retirement or
$350,000 five years after the date of your retirement.
(a) If the interest rate is 0% per year, which alternative should you choose?
Take the money now.
Waiting until 5 years after retirement.
1.00 points out of 1.00
The correct answer is: Waiting until 5 years after retirement.
(b) If the interest rate is 8% per year, which alternative should you choose?
Take the money now.
Waiting until 5 years after retirement.
1.00 points out of 1.00
The correct answer is: Take the money now.
(c) If the interest rate is 20% per year, which alternative should you choose?
Take the money now.
Waiting until 5 years after retirement.
1.00 points out of 1.00
The correct answer is: Take the money now.
Hint: PV = FV ÷ (1+r)n
(a) PV = $350,000 ÷ (1+0%)5
(b) PV = $350,000 ÷ (1+8%)5
(c) PV = $350,000 ÷ (1+20%)5
Question 7
Correct
1.00 points out of 1.00
You have been offered a unique investment opportunity. If you invest $20,000 today, you will receive $1,000
one year from now, $3,000 two years from now, and $20,000 ten years from now.
(a) The NPV of the opportunity if the interest rate is 10% per year is $ -8901
. (Round to the nearest
dollar.)
Should you take the opportunity
Reject it because the NPV is less than 0.
Take it because the NPV is equal or greater than 0.
1.00 points out of 1.00
The correct answer is: Reject it because the NPV is less than 0.
(b) The NPV of the opportunity if the interest rate is 6% per year is $ -5219
. (Round to the nearest
dollar.)
Should you take the opportunity
Reject it because the NPV is less than 0.
Take it because the NPV is equal or greater than 0.
1.00 points out of 1.00
The correct answer is: Reject it because the NPV is less than 0.
Hint: NPV = PV (All Cash Flows).
(a) NPV = PV(-$20,000 today) + PV ($1,000 in one year) + PV ($3,000 in two years) + PV ($20,000 in 10
years) = -$20,000 + $1,000 / (1+10%) + $3,000 / (1+10%)2 + $20,000 / (1+10%)10
(b) NPV = PV(-$20,000 today) + PV ($1,000 in one year) + PV ($3,000 in two years) + PV ($20,000 in 10
years) = -$20,000 + $1,000 / (1+6%) + $3,000 / (1+6%)2 + $20,000 / (1+6%)10
Question 8
Correct
1.00 points out of 1.00
What is the present value of $5,000 paid at the end of each of the next 78 years if the interest rate is 9% per
year?
The present value is $ 55489
. (Round to the nearest dollar.)
Hint: The stream of cash flows described above is a standard Annuity. Therefore, you can apply directly the
Present Value formula for Annuity.
Identify C, r and n, and use PV = C/r × [ 1 - 1/(1+r)n ].
PV = $5,000 / 9% × [ 1 - 1/(1+9%)78 ].
Question 9
Correct
2.00 points out of 2.00
What is the present value of $5,000 paid at the beginning of each of the next 78 years if the interest rate is 9%
per year?
The present value is $ 60483
. (Round to the nearest dollar.)
Hint: The cash flow at t=0 is $5,000 and the last cash flow stops at the end of 77 years (that is, the beginning of
78 years). Therefore, the stream is not a standard annuity model. The timeline can be split into two parts:
$5,000 cash flow at t=0 and a 77-year annuity of $5,000 cash flows.
Total PV = $5,000 today + PV (77-year Annuity)
Total PV = $5,000+ $5,000 / 9% × [ 1 - 1/(1+9%)77 ].
Question 10
Correct
1.00 points out of 1.00
Your lender now offers you a 30-year fixed-rate home mortgage with 3.6% interest per year. If you can afford
a monthly payment of $3,000, what is maximum price of a house that you can afford?
The maximum house price is $ 659855
. (Round to the nearest dollar.)
Hint: This is a question on affordability. The maximum amount of loan that you can take out equals to the
present value of the 360-month annuity.
t=0
t=1
t=2
t=3
t=360
|----------------|----------------|----------------|----- ··············-----|
$0
$3000
$3000
$3000
$3000
The maximum monthly payment C = $3,000.
the monthly interest rate can be derived from annual rate: rm= r ÷ 12 = 3.6% ÷ 12 = 0.3% =0.003.
n = 30 years × 12 = 360 month.
Apply the PV formula for annuity and you can figure out the max affordable loan.
PV = $3000 / 0.003 * [1 - 1 / (1+0.003)^360]
Question 11
Correct
1.00 points out of 1.00
When you purchased your house, you took out a 30-year mortgage with an interest rate of 4.8% per year. The
monthly payment on the mortgage $1,500. You have just made a payment and have now decided to pay the
mortgage off by repaying the outstanding balance.
What is the payoff amount if you have lived in the house for 18 years (so there are 12 years left on the
mortgage)? Payoff amount is $ 163954
. (Round to the nearest dollar.)
Hint: Given a monthly payment of $1,500, the payoff amount is equal to the present value of an n-month
annuity, n being the number of monthly payments remaining on the mortgage.
There are 144 (=12×12) months left. The timeline can be drawn:
t=0
t=1
t=2
t=3
t=144
|----------------|----------------|----------------|----- ··············-----|
$0
$1500
$1500
$1500
$1500
The monthly interest rate is: rm = r ÷ 12 = 4.8% ÷ 12 = 0.4% = 0.004
The present value of 144-month annuity is: PV = $1,500 ÷ 0.004 × [ 1 - 1 ÷ (1+0.004)144 ] = $163,954
Question 12
Correct
1.00 points out of 1.00
You bought a house worth $900,000 and the loan is a 30-year fixed rate mortgage with 4.5% annual interest
rate. What is your monthly payment?
Your monthly payment is $ 4560
. (Round to the nearest dollar.)
Hint: The loan is a 360-month annuity. The present value of the annuity equals to the loan amount, so PV =
$900,000.
t=0
t=1
t=2
t=3
t=360
|----------------|----------------|----------------|----- ··············-----|
$0
$C
$C
$C
$C
C = unknown.
Monthly Interest rate: rm= r ÷ 12 = 4.5% ÷ 12 = 0.375% =0.00375.
n = 30 years × 12 = 360.
We have an equation with one unknown. Use the present value formula of annuity, back out C.
$900,000 = c / 0.00375 * [1 - 1 / (1+0.00375)^ 360]
Question 13
Correct
1.00 points out of 1.00
You just purchased a car for $24,000 and the auto loan is 60-month fixed rate loan with annual interest of
2.4%. What is your monthly payment?
Your monthly payment is $ 425
. (Round to the nearest dollar.)
Hint: The auto loan is a 60-month annuity with monthly cash flow of $C and monthly interest rate of 0.2%
(=2.4%÷12). Given that the present value is $24,000, you can back out $C.
$24,000 = C / 0.002 * [ 1 - 1 / (1+0.002)^60]
t=0
t=1
t=2
t=3
t=60
|----------------|----------------|----------------|----- ··············-----|
$0
$C
$C
$C
$C
Question 14
Correct
1.00 points out of 1.00
You are 22 years old and decide to start saving for your retirement. You plan to save $6,000 at the end of each
year (so the first deposit will be one year from now), and will make the last deposit when you retire at age 65.
Suppose you earn 6% per year on your retirement savings.
How much will you have saved for retirement right at age 65?
$ 1125045
. (Round to the nearest dollar.)
Hint: This is a question about the future value of an annuity. First figure out the present value of this 43-year
annuity; then get the future value by compounding the present value with a factor of (1+r)43.
Constant Cash Flow: C = $6,000.
Annual Interest Rate: r = 0.06.
n = 65 - 22 = 43.
FV = PV * (1+r)^n = 6000 / 0.06 * [ 1 - 1 / (1+0.06)^43 ] * (1+0.06)^43
age 22
23
24
25
65
t=0
t=1
t=2
t=3
t=43
|----------------|----------------|----------------|----- ··············-----|
$0
$6000
$6000
$6000
$6000
Question 15
Correct
1.00 points out of 1.00
Your grandmother has been putting $2,000 into a savings account on every birthday since your first (that is,
when you turned 1). The account pays an interest rate of 5%. How much money will be in the account on your
18th birthday immediately after your grandmother makes the deposit on that birthday?
The amount in the account upon your 18th birthday is $ 56265
. (Round to the nearest dollar.)
Hint:
This is an 18-year annuity of annual cash flow of $2,000 and annual interest rate of 5%. First, compute the
present value of the annuity (back to the point when you are born); then, multiply the PV with a factor of
(1+r)n to get FV.
C = $2000; r=0.05; n= 18
t=0
t=1
t=2
t=3
t=18
|----------------|----------------|----------------|----- ··············-----|
$0
$2000
$2000
$2000
San Francisco State University
A California State University
Campus
$2000
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