Week 3 Practice Problems
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5-1. 1. Your bank is offering you an account that will pay 20% interest in total for a two-year deposit.
Determine the equivalent discount rate for a period length of
six months.
one year.
one month.
a.
Since six months is
6
1
24
4
of two years, using our rule
1
4
1
0.2
1.0466
the equivalent six-month
rate is 4.66%.
b.
Since one year is half of two years
1
2
1.2
1.0954
, the equivalent one-year rate is 9.54%.
c.
Since one month is
1
24
of two years, using our rule
1
24
1
0.2
1.00763
, the equivalent one-month
rate is 0.763%
5-10.
10. Excel Project and Excel Solution Your son has been accepted into university. This university guarantees
that your son’s tuition will not increase for the four years that he attends. The first $10,000 tuition payment
is due in six months. After that, the same payment is due every six months until you have made a total of
eight payments. The university offers a bank account that allows you to withdraw money every six months
and has a fixed APR of 4% (with semiannual compounding) guaranteed to remain the same over the next
four years. How much money must you deposit today if you intend to make no further deposits and would
like to make all the tuition payments from this account, leaving the account empty when the last payment is
made?
Timeline:
0
1
2
1
4
0
1
2
8
10,000
10,000
10,000
4% APR (semiannual) implies a semiannual discount rate of
4%
2%
2
.
So,
8
10,000
1
PV
1
0.02
1.02
$73, 254.81
.
7-10.
10. DFB Inc. expects earnings this year of $5 per share, and it plans to pay a $3 dividend to
shareholders. DFB will retain $2 per share of its earnings to reinvest in new projects with an expected
return of 15% per year. Suppose DFB will maintain the same dividend payout rate, retention rate, and
return on new investments in the future and will not change its number of outstanding shares.
What growth rate of earnings would you forecast for DFB?
If DFB’s equity cost of capital is 12%, what price would you estimate for DFB stock?
Suppose DFB instead paid a dividend of $4 per share this year and retained only $1 per share in earnings. If
DFB maintains this higher payout rate in the future, what stock price would you estimate now? Should
DFB raise its dividend?
a.
Eq. 7.12: g = retention rate × return on new investments = (2/5) × 15% = 6%
b.
P = 3 / (12% – 6%) = $50
c.
g = (1/5) × 15% = 3%, P = 4 / (12% – 3%) = $44.44. No, projects are positive NPV (return exceeds
cost of capital), so don’t raise the dividend as it will cause the stock price to drop in this case.
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Related Questions
3. Your bank is offering you an account that will pay 10% interest in total for a two-yeardeposit. Determine the equivalent discount rate for a period length of:a. Six months.b. One year.
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K
Your bank is offering you an account that will pay 23% interest (an effective two-year rate) in total for a two-year
deposit. Determine the equivalent discount rate for the following periods:
a. Six months
b. One year
c. One month
(Note: Be careful not to round any intermediate steps less than six decimal places.)
a. Six months
The equivalent discount rate for a period length of six months is%. (Round to two decimal places.)
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Determine the equivalent discount rate for the following periods:
a. Six months
b. One year
c. One month
(Note: Be careful not to round any intermediate steps less than six decimal places.)
+
a. Six months
The equivalent discount rate for a period length of six months is%. (Round to two decimal places.)
xample Get more help.
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MacBook Pro
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Your bank is offering you an account that will pay 19% interest (an effective two-year rate) in total for a two-year deposit. Determine the equivalent discount rate for the
following periods:
a. Six months
b. One year
c. One month
(Note: Be careful not to round any intermediate steps less than six decimal places.)
a. Six months
The equivalent discount rate for a period length of six months is %. (Round to two decimal places.)
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You are able to make a current deposit in the amount of
$21,605.49. The expected discount rate is 9.6%. Interest is
earned on an annual basis. The time period is 10 years.
What is the size of the annual withdrawal possible under
these circumstances? a. $2,160.54 b. $3465.00 c. $3,456.00
d. $4,356.00
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1.What is the effective interest rate of a simple discount note for $4,500 at a bank discount rate of 14% for 24 months? (Round to the nearest tenth percent.)
A. 14.0%
B. 19.4%
C. 28.0%
D. 38.9%
2.Use the ordinary interest method to find the rate of interest that Make Over Picture Photo pays on a loan of $8,000 for 265 days, if the amount of interest is $510.00. (Round your answer to the nearest tenth percent.)
A. 7.5%
B. 8.4%
C. 8.5%
D. 8.7%
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1. How much interest will be charged on 7,300 borrowed for three (3) years at a simple interest rate of 12% per annum?
2. If a nine-month term deposit at a bank earns a simple interest rate of 9% per annum, how much should be deposited to earn 225 of interest?
3. How long will 3,000 accumulate to 5,000 if the discount rate is 4%?
4. Find the actual and approximate time from november 18, 2015 to may 9, 2016.
5. SSS limited paid a dividend of 434 per share last year. If yesterday's last price was 4,650, what is the current yield on the stock?
6. MMD Enterprise is currently selling at 1,780 with a dividend of 140. What is the current yield of the stock?
7. Millet purchases 340 shares of De Leon Company common stock 5,230 per share. A few months later, she sells the shares at 6,100. Her stockbroker charges 4.3% commission on round lots and 4.9% on odd lots. Compute for the following:
a. Total cost
b. Proceeds
c. Gain or loss on the transaction
4. Sharlene purchases 280 shares of SJS…
arrow_forward
The final payment will be $______ (Round to the nearest cent.)
Your bank is offering you an account that will pay 20% interest in total for a two-year deposit. Determine the equivalent discount rate for the following:
a. Six months
b. One year
c. One month
(Note: Be careful not to round any intermediate steps less than six decimal places.)
a. Six months
The equivalent discount rate for a period length of six months is _____%. (Round to two decimal places.)
Part 2
b. One year
The equivalent discount rate for a period length of one year is _____%. (Round to two decimal places.)
Part 3
c. One month
The equivalent discount rate for a period length of one month is ______%. (Round to three decimal places.)
arrow_forward
4) Find the account balance at the end of 10 years, if you deposit 15,000 in an account today if a. The bank
pays interest at 12% per year. b. The bank pays interest at 6% every 6 months. c. The bank pays interest at
3% per quarter, d. The bank pays interest at 1% per month. What do you observe when you compare the
balances for the four scenarios listed.
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2. If a nine-month term deposit at a bank earns a simple interest rate of 9% per annum, how much
should be deposited to earn P225 of interest?
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Suppose a bank offers to lend you $10,000 for 1 year on a loan contract that calls for you to make interest payments
of $350.00 at the end of each quarter and then pay off the principal amount at the end of the year. What is the
effective annual rate on the loan?
14.75%
13.28%
12.39%
11.21%
15.34%
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8. You can earn $38 in interest on a $1000 deposit for eight months. If the EAR is the same regard-
less of the length of the investment, determine how much interest will you earn on a $1000
deposit for
a. 9 months.
Sunnon
0
b. 1 year.
c. 1.6 years.
met $101 in a bank account and five years later it has grown to $136.14.
arrow_forward
1. Five years from today, you would like to withdraw $5,000 from an account that pays an
interest rate of 5% per year. How much do you need to deposit in the account one year from
today in order to make the withdrawal?
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5. How much should be deposited in an account yielding 8% compounding weekly to obtain $14,900 in
seven years and five months?
6. $37.500 is deposited in an account paying 54% compounded monthly. How much will be in the account
after eight years and five months?
7. $49,300 is kept in an account paying 5.21% compounded daily. How much will be in the account after
10 years?
8. At what interest rate, compounded daily, will $5,000 grow to SS,00o in seven years and five months?
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4. You want to deposit $600 in a savings account. Account A earns 3.5% simple interest per
year. Account B earns 3.3% interest compounded annually.
a. Which account should you choose if you invest your money for 3 years? 6 years? Explain.
b. After how many years is the balance in Account B greater than the balance in Account A?
c. After how many years is the difference between the account balances greater than $5?
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Assume you make a single deposit of $1000 into a savings account that pays interest at 0.5% per month. If you want to know how much the accountwill be worth in 5 years, the only values you can use for i and n area. Effective i per month and n = 60b. Effective i per quarter and n = 30c. Effective i per semiannual period and n = 10d. Either (a) or (c)
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2.60. You have borrowed $10,000 from a bank at the interest rate of 1% per month. Your
monthly payment is $554.15. Find the time required to repay the loan.
arrow_forward
An interest problem:
Suppose $1000 is invested in an account paying interest at a continuous rate of 6% a year.
What is the A.P.R. for this loan?
A. 6%
B. 6.18%
C. 5.82%
D. 1.06
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6. Calculate the simple interest due on a four-month loan of $900 if the interest rate is 2.2% per month?
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Your bank is offering you an account that will pay 20% interest in total for a two-year deposit. Determine the equivalent discount rate for a period length of 1 year, 6 months, & 1 year?
arrow_forward
Listen
How long would you have to wait for a deposit of $1,625 to earn $34 in interest?
Assume that the account earns a simple interest rate of 6.75% per annum.
Express your answer in months to two decimal places.
Your Answer:
Answer
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7. The remainder on a home loan is refinanced by a bank. The refinanced loan is a 15-year loan for
$176,200 scheduled to be paid off using monthly payments. The annual percentage rate for the
loan is 3.15%
a. Identify the APR for this loan in decimal form. Use four decimal place accuracy.
b. Identify the number of payments per year used in the loan payment formula.
C.
Calculate the monthly payment required to pay off this loan.
d. Calculate the total amount of all the payments required to pay off this loan.
e. Calculate the total amount paid towards interest after the loan is paid off.
f. Calculate the percentage of the total amount that is paid towards interest.
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PROBLEMS
1. What is the annual rate of interest if P265 is earned in four
months on an investment of P15,000?
Ans. 5.3%
2. A loan of P2,000 is made for a period of 13 months, from
January 1 to January 31 the following year, at a simple interest rate
of 20%. What future amount is due at the end of the loan period?
Ans. P2.433.33
3. If you borrow money from your friend with simple interest of
12%, find the present worth of P20,000, which is due at the end of
nine months.
Ans. P18.348.62
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3. You have a bank deposit now worth $5000. How
long will it take for your deposit to be worth more than
$8000 if:
(a) The account pays 5 percent actual (per sub-period)
interest every half-year and is compounded every half-
year?
(b) The account pays 5 percent nominal interest,
, compounded semiannually?
arrow_forward
7. If you want to collect ¢ 5,000,000 in 4 years and for this you make deposits every end of the month in the local bank that pays 18% interest compounded monthly. After 3 years, the bank lowers the interest to 15%. What is the value of each deposit, before and after the change in the interest rate?
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If you deposit $100 in a savings account at the end of each month for 2 years, the balance will be a function f (r) of the interest rate, r%. At 7% interest (compounded monthly), f (7) = 2568.10 and f (7) = 25.06. Approximately how much additional money would you earn if the bank paid 7 1/2 % interest?
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K
What is the effective interest rate of a simple discount note for $27,100, at an ordinary bank
discount rate of 16%, for 10 days? Assume that there are 360 days in a year.
The effective interest rate is %.
(Round to the nearest tenth as needed.)
In
m
ac
cogr
(Co
tate
arrow_forward
k. Five banks offer nominal rates of 9% on deposits, but A pays interest annually, B pays semiannually, C pays quarterly, D pays monthly, and E pays daily. Assume 365 days in a year.
1. What effective annual rate does each bank pay? If you deposit $6,000 in each bank today, how much will you have in each bank at the end of 1 year? 2 years? Round your
answers to two decimal places.
A
E
EAR
%
%
%
%24
24
FV after 1 year
$
$4
2$
$4
FV after 2 years
%24
2$
$
2. If the TVM is the only consideration, what nominal rate will cause all of the banks to provide the same effective annual rate as Bank A? Round your answers to two decimal
places.
A-Z
office
Nominal rate
%
%
%
%
3. Suppose you don't have the $6,000 but need it at the end of 1 year. You plan to make a series of deposits – annually for A, semiannually for B, quarterly for C, monthly for D,
and daily for E– with payments beginning today. How large must the payments be to each bank? Round your answers to the nearest cent.
A
D
Payment
$4…
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Suppose you deposited $41,000 in a bank account that pays 5.75% with daily compounding based on a 360-day year. How much would be in the account after 8 months, assuming each month has 30 days?
a. $42,598.28
b. $42,571.67
c. $43,426.30
d. $42,793.66
e. $42,602.05
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You just deposited $6,500 in a bank account that pays a 4.0% nominal interest rate, compounded quarterly. If you also add another $5,000 to the account one year (4 quarters) from now and another $7,500 to the account two years (8 quarters) from now, how much will be in the account three years (12 quarters) from now? Select the correct answer.
a. 26,058.29
b. 26,040.89
c. 26,006.09
d. 26,023.49
e. 26,075.69
arrow_forward
Suppose that you deposit $750 into a bank account today. If the bank pays 8 percent APR per year, compounded quarterly, how much will be in the account at the end of 4 years.A. $812 84B. $750.00C. $1,029.59D. $927.52E. $1.020.37
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4. What is the simple interest to the nearest cent on a credit card balance of $1,150.00 at 11% interest for 3 months?
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A bank pays simple interest at the rate of 8% per year for certain deposits. If a customer deposits P10,000 and make no withdrawal for three years what is the interest earned in that period of time?
A person borrow P100,000 for a period of 6 months. What simple interest rate is being charged if the amount A that must be paid after 6 months is P104,500?
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