Math 034 First Letter of Last Name
Homework #7 Full Name ___________________________
Due Wednesday 10/28/15 Section _____________________________
1. (Section 6.3) Suppose that Lily, Joshua, and Burt own a bike shop that they have set up as a business
partnership. They agree to distribute their profits in unequal shares because Joshua works the most hours and
Burt does the accounting. They agree to distribute the profits as follows: Lily (7 parts), Joshua (12 parts), Burt
(11 parts). The bike shop earned $32,000 last month. How much does each person receive?
2. (Section 6.3) Fastlane Car Rental earned $835,000 in the last quarter, and the company’s management declared
a dividend of $405,000. The company has 540,000 shares of stock issued. If you own 164 shares, how much will
you receive as a dividend?
3. (Section 7.1) Mocha Crunch Bakery paid its shareholders a dividend of $1.12 per share in the last quarter and
$4.25 per share in the last year. The market price per share of Mocha Crunch Bakery is currently $36.59.
a. Calculate the stock’s current dividend yield.
b. Calculate the stock’s trailing dividend yield.
4. (Section 7.1) Eleven years ago, I invested $10,000 in the stock of Butterfly Hollow Corporation. I sold the stock
today for $14,195. What compound annual growth rate does this represent?
5. (Section 7.1) Nine years ago, I bought stock in Clementine Enterprises for $20.25 per share. The stock has split 2
for 1 twice, and now trades for $14.05 per share. What compound annual growth rate does my capital gain
represent?
6. (Section 7.1) Fifteen years ago, I invested $2,500 in a dividend reinvestment plan offered by my local electric
utility company. The value of my original investment, including reinvested dividends, has grown to $4,746.16.
What was my total rate of return?
7. (Section 7.2) On September 1, 2015, Havershire Inc. issued a $5,000 par value bond with a 3% coupon rate and a
September 1, 2030 maturity date. Interest will be paid semiannually. How much total interest will the owner of
this bond receive?
8. (Section 7.2) Viking Shield
Solution
s issued a $2,000 par value bond with a 4 3/8% coupon rate. Interest
payments are made semiannually. Suppose that one of these bonds sells for $1,950.79. What is the current
yield?
9. (Section 7.2) Alicia’s grandmother bought a $100 face value savings bond for $50 when Alicia was born. On
Alicia’s 21
st
birthday, she cashed the bond in for $141.20. What effective rate of compound interest did she earn
on this bond?
Trial Balance-EntriesBig Ed's Motorcycle ShopEnd of Period WorksheetFor the period ending 12/31/2015Unadjusted Trial BalanceAdjusting EntriesAdjusted Trial BalanceIncome StatementBalance SheetDRCRDRCRDRCRDRCRDRCRCash184,500Accounts Receivable145,200Merchandise Inventory, Parts100,000Merchandise Inventory, Motorcycles110,000Office Supplies6,720Prepaid Insurance4,080Office ...
Math 034 First Letter of Last Name Homework #7 .docx
1. Math 034 First Letter of Last Name
Homework #7 Full Name ___________________________
Due Wednesday 10/28/15 Section
_____________________________
1. (Section 6.3) Suppose that Lily, Joshua, and Burt own a bike
shop that they have set up as a business
partnership. They agree to distribute their profits in unequal
shares because Joshua works the most hours and
Burt does the accounting. They agree to distribute the profits as
follows: Lily (7 parts), Joshua (12 parts), Burt
(11 parts). The bike shop earned $32,000 last month. How
much does each person receive?
2. (Section 6.3) Fastlane Car Rental earned $835,000 in the last
quarter, and the company’s management declared
a dividend of $405,000. The company has 540,000 shares of
stock issued. If you own 164 shares, how much will
you receive as a dividend?
3. (Section 7.1) Mocha Crunch Bakery paid its shareholders a
dividend of $1.12 per share in the last quarter and
$4.25 per share in the last year. The market price per share of
Mocha Crunch Bakery is currently $36.59.
a. Calculate the stock’s current dividend yield.
b. Calculate the stock’s trailing dividend yield.
2. 4. (Section 7.1) Eleven years ago, I invested $10,000 in the
stock of Butterfly Hollow Corporation. I sold the stock
today for $14,195. What compound annual growth rate does
this represent?
5. (Section 7.1) Nine years ago, I bought stock in Clementine
Enterprises for $20.25 per share. The stock has split 2
for 1 twice, and now trades for $14.05 per share. What
compound annual growth rate does my capital gain
represent?
6. (Section 7.1) Fifteen years ago, I invested $2,500 in a
dividend reinvestment plan offered by my local electric
utility company. The value of my original investment,
including reinvested dividends, has grown to $4,746.16.
What was my total rate of return?
7. (Section 7.2) On September 1, 2015, Havershire Inc. issued a
$5,000 par value bond with a 3% coupon rate and a
September 1, 2030 maturity date. Interest will be paid
semiannually. How much total interest will the owner of
this bond receive?
8. (Section 7.2) Viking Shield
Solution
3. s issued a $2,000 par value bond with a 4 3/8% coupon rate.
Interest
payments are made semiannually. Suppose that one of these
bonds sells for $1,950.79. What is the current
yield?
9. (Section 7.2) Alicia’s grandmother bought a $100 face value
savings bond for $50 when Alicia was born. On
Alicia’s 21
st
birthday, she cashed the bond in for $141.20. What effective
rate of compound interest did she earn
on this bond?
Trial Balance-EntriesBig Ed's Motorcycle ShopEnd of Period
WorksheetFor the period ending 12/31/2015Unadjusted Trial
BalanceAdjusting EntriesAdjusted Trial BalanceIncome
StatementBalance
SheetDRCRDRCRDRCRDRCRDRCRCash184,500Accounts
Receivable145,200Merchandise Inventory,
Parts100,000Merchandise Inventory, Motorcycles110,000Office
6. Nth Term of An Arithmetic Sequence an = a1 + (n – 1)d
a1 = first term
d = common difference
Sum of the First n Terms of an Arithmetic Sequence
Sn = (n/2)(a1 + an)
a1 = first term
an = nth term
Simple Discount Formula D = MdT
D = simple discount
M = maturity value
7. d = simple discount rate
T = term
Compound Interest Formula FV = PV(1 + i)
n
FV = future value
PV = present value
i = interest rate per compounding period
n = number of compounding periods
N+1
st
Term of a Geometric Sequence an = a0 r
n
a0 = first term
8. a1 = second term
r = common ratio = a1/a0
Sum of the First n Terms of a Geometric Sequence
Sn = a0 (1 – r
n
) / (1 – r)
a0 = first term
r = common ratio = a1/a0
Infinite Geometric Sum
S∞ = a0 /(1 – r)
a0 = first term
r = common ratio = a1/a0
9. Compound Interest Rate
i = compound interest rate
FV = future value
PV = present value
n = number of compounding periods
Time Periods n = log (FV/PV)
log (1 + i)
i = compound interest rate
FV = future value
PV = present value
10. Rule of 72
The time required for a sum of money to double at
a compound interest rate of x% is approximately
72/x years. (x should not be converted to a decimal)
Rule of 72 (Alternate Form)
The compound interest rate required for a sum of money
to double in x years is approximately 72/x percent.
11. Effective Interest Rate Eff. Rate = (1 + r/c)
c
– 1
r = the nominal interest rate
c = the number of compoundings per year
Continuous Compounding FV = PV e
(rt)
FV = future value
PV = present value
e = a mathematical constant (approx. 2.71828)
r = annual interest rate
t = number of years
12. Future Value Annuity Factor sn/i =
i = interest rate per payment period
n = number of payment periods
Future Value of an Ordinary Annuity FV = PMTsn/i
FV = future value of the annuity
PMT = amount of each payment
sn/i = annuity factor
Future Value of an Annuity Due FV = PMTsn/i(1 + i)
FV = future value of the annuity
PMT = amount of each payment
i = interest rate per payment period
sn/i = annuity factor
13. Interest for Future Value Annuities
interest = FV – total deposits
Present Value Annuity Factor
i = interest rate per payment period
n = number of payment periods
Present Value of an Ordinary Annuity PV = PMTan/i
PV = present value of the annuity
PMT = amount of each payment
an/i = present value annuity factor
Present Value of an Annuity Due PV = PMTan/i(1 + i)
14. PV = present value of the annuity
PMT = amount of each payment
an/i = present value annuity factor
Interest for Present Value Annuities
interest = total deposits – PV
1/
( ) 1
nFV
i
PV
i
16. Sales Tax T = P(1 + r)
T = total price including tax
P = price before tax
r = sales tax rate
T – P = amount of tax
Income Tax Formulas
Annual taxable income
= annual income – benefits – exemptions – deductions
Paycheck taxable income
= paycheck income – benefits – exemptions
17. FICA taxes based on paycheck income – benefits
Dividends
dividend per share = total dividend
total # shares
individual dividend
= (dividend per share)(# individual shares)
current dividend yield = quarterly dividend per share × 4
market price per share
trailing divided yield = trailing dividend per share
market price per share
18. Compound Annual Growth Rate
or Rate of Return
i = compound growth rate
FV = future value
PV = present value
n = number of years
Net Asset Value (NAV)
NAV = total assets / total number of shares
Mutual Fund Shares
# shares = amount invested / NAV
19. Inflation Formula FV = PV(1 + i)
n
FV = future value of an item
PV = present value of an item
i = rate of inflation
n = number of time periods
Declining Balance Depreciation FV = PV(1 + i)
n
FV = future value
PV = present value
i = depreciation rate
n = years
20. Straight Line Depreciation
Total depreciation amount
= Original value – Residual value
Annual depreciation = Total depreciation amount
Useful Life
Depreciated value
= Original value – (# of years)(Annual depreciation)
Credit Card Interest I = PRT
I = interest
P = principal
21. R = interest rate
T= term
Mortgage Formulas
Equity = value of home – amount of mortgage
Total PITI = principal + interest + taxes + insurance(s)
One point = 1% of the amount of the loan
Payback period = cost of points / monthly savings
The 28% Rule
Total PITI cannot exceed 28% of gross monthly income.
The 36% Rule
Total PITI and all other long-term debt payments cannot
22. exceed 36% of gross monthly income.
Lease Payment = Payment on Loss +
Interest on Residual
Payment on loss: Use PV = PMTan/i where
PV = original price – residual value
Interest on residual: Use I=PRT where P = residual value
Markup Based on Cost P = C(1 + r)
P = selling price
C = cost
r = percent markup
23. Markup Based on Selling Price C=SP(1 – r)
C = item’s cost
SP = selling price
r = gross profit margin
Markdown MP = OP(1 – d)
MP = marked-down price
OP = original price
d = percent markdown
Profit Margin Formulas
Gross profit = sales – cost
Gross profit margin = gross profit / sales
24. Gross profit = (gross profit margin)(sales)
Net profit = sales – cost – expenses
Net profit margin = net profit / sales
Cost-Revenue Analysis
P = R – C
P = profit function
R = revenue function
C= cost function
1/
( ) 1
nFV
i
