Math 034 First Letter of Last Name Homework #8 Full Name ___________________________ Due Wednesday 11/4/15 Section _____________________________ 1. (Section 7.3) On the basis of how long he has until retirement and his comfort with investment risk, Bill has decided that he wants to allocate the money in his retirement account as follows: 70% to equities, 25% to fixed income, and 5% to cash. a. If he assumes that each asset class provides the low end of the rates of return shown in the table in Example #1 in the PowerPoint slides from Section 7.3, what overall rate of return would he expect to earn over the long term? b. If he assumes that each asset class provides the high end rate of return, what overall rate of return would he expect to earn over the long term? 2. (Section 7.3) The Northern Tier Real Estate Fund has $84,324,980 in assets and 1,009,880 shares. If Ruth owns 76.387 shares of this fund, what is the value of her investment? 3. (Section 7.3) The net asset value of a mutual fund is $139.56. The fund charges a 2% load. How many shares will you own if you invest $11,000 in this fund? 4. (Section 7.3) One November 1, 2009, the net asset value of the Phillips International Fund was $52.43. On November 1, 2015, the net asset value was $28.12. If all dividends were reinvested, each share of the fund on November 1, 2009 would have grown to 2.486 shares on November 1, 2015. Calculate the average annual rate of return. 5. (Section 7.3) A mutual fund had annual returns of +10%, +9%, -4%, -8%, and +3% in each of the past 5 years. What was the average rate of return over this period? 6. (Section 7.3) Two years ago, an investment you made in a mutual fund was worth $7,500.00. Today it is worth $6,195.35. When you complain to your fund manager, he indicates that your annual rate of return for the year that just ended was 8%. Calculate your annual rate of return for the first year. 7. (Section 8.1) The company you work for provides a lifetime income to its employees on retirement at age 65. The formula provides 2% for each year of service of the average of the employee’s earnings for the last 3 years on the job, up to a maximum of 75%. Your company offers employees the choice to retire as early as age 60 or as late as age 72. Those retiring before age 65 have their calculated benefit reduced by 2.4% for each year they retire prior to age 65; those retiring later have their benefit increased by 2.2% for each year beyond age 65 that they work. a. Suppose you plan to retire this year at age 61. You have 26 years of service to the company and your last 3 years’ earnings were $55,785, $59,840, and $60,565. Calculate your pension benefit. b. Suppose you plan to retire this year at age 70. You have 40 years of service to the company and your last 3 years’ earnings were $67,654, $69,450, and $74,820. Calculate your pension benefit. 8. (Section 8.1) The comp ...

1. Math 034 First Letter of Last Name
Homework #8 Full Name ___________________________
Due Wednesday 11/4/15 Section
_____________________________
1. (Section 7.3) On the basis of how long he has until retirement
and his comfort with investment risk, Bill has
decided that he wants to allocate the money in his retirement
account as follows: 70% to equities, 25% to fixed
income, and 5% to cash.
a. If he assumes that each asset class provides the low end of
the rates of return shown in the table in
Example #1 in the PowerPoint slides from Section 7.3, what
overall rate of return would he expect to
earn over the long term?
b. If he assumes that each asset class provides the high end rate
of return, what overall rate of return
would he expect to earn over the long term?
2. (Section 7.3) The Northern Tier Real Estate Fund has
$84,324,980 in assets and 1,009,880 shares. If Ruth owns
76.387 shares of this fund, what is the value of her investment?
3. (Section 7.3) The net asset value of a mutual fund is
$139.56. The fund charges a 2% load. How many shares
will you own if you invest $11,000 in this fund?

2. 4. (Section 7.3) One November 1, 2009, the net asset value of
the Phillips International Fund was $52.43. On
November 1, 2015, the net asset value was $28.12. If all
dividends were reinvested, each share of the fund on
November 1, 2009 would have grown to 2.486 shares on
November 1, 2015. Calculate the average annual rate
of return.
5. (Section 7.3) A mutual fund had annual returns of +10%,
+9%, -4%, -8%, and +3% in each of the past 5 years.
What was the average rate of return over this period?
6. (Section 7.3) Two years ago, an investment you made in a
mutual fund was worth $7,500.00. Today it is worth
$6,195.35. When you complain to your fund manager, he
indicates that your annual rate of return for the year
that just ended was 8%. Calculate your annual rate of return for
the first year.
7. (Section 8.1) The company you work for provides a lifetime
income to its employees on retirement at age 65.
The formula provides 2% for each year of service of the average
of the employee’s earnings for the last 3 years
on the job, up to a maximum of 75%. Your company offers
employees the choice to retire as early as age 60 or
as late as age 72. Those retiring before age 65 have their
calculated benefit reduced by 2.4% for each year they
retire prior to age 65; those retiring later have their benefit
increased by 2.2% for each year beyond age 65 that
they work.

3. a. Suppose you plan to retire this year at age 61. You have 26
years of service to the company and your
last 3 years’ earnings were $55,785, $59,840, and $60,565.
Calculate your pension benefit.
b. Suppose you plan to retire this year at age 70. You have 40
years of service to the company and your
last 3 years’ earnings were $67,654, $69,450, and $74,820.
Calculate your pension benefit.
8. (Section 8.1) The company that Renee works for contributes
9% of each employee’s annual earnings to a defined
contribution plan, provided that the employee contributes at
least 6%. Renee earns $47,750 per year. How
much will go into her retirement account this year if she
contributes:
a. 4% of her income?
b. 8% of her income?
9. (Section 8.1) Jana is leaving her job after working for her
company for 5 ½ years. She has contributed a total of
$24,684.13 to her retirement account. The total amount in her
retirement account is $38,987.84. Using the
vesting table found in Example #6 in the PowerPoint slides for
Section 8.1, find her vested balance in this plan.
MATH 034 Formulas

4. Simple Interest Formula I = PRT
I = simple interest
P = principal
R = simple interest rate
T= term
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

5. 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
a1 = second term
r = common ratio = a1/a0
Sum of the First n Terms of a Geometric Sequence
Sn = a0 (1 – r
n

6. ) / (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
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

7. PV = present value
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.
Effective Interest Rate Eff. Rate = (1 + r/c)
c
– 1
r = the nominal interest rate
c = the number of compoundings per year

8. 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
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)

9. FV = future value of the annuity
PMT = amount of each payment
i = interest rate per payment period
sn/i = annuity factor
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)
PV = present value of the annuity
PMT = amount of each payment

10. an/i = present value annuity factor
Interest for Present Value Annuities
interest = total deposits – PV
1/
( ) 1
nFV
i
PV
i
i
n
i
i
a
n
in

11. )1(1
/
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

12. 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
Compound Annual Growth Rate
or Rate of Return
i = compound growth rate
FV = future value
PV = present value

13. n = number of years
Net Asset Value (NAV)
NAV = total assets / total number of shares
Mutual Fund Shares
# shares = amount invested / NAV
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

14. n = years
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
R = interest rate
T= term
Mortgage Formulas

15. 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
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

16. C = cost
r = percent markup
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
Gross profit = (gross profit margin)(sales)
Net profit = sales – cost – expenses
Net profit margin = net profit / sales

17. Cost-Revenue Analysis
P = R – C
P = profit function
R = revenue function
C= cost function
1/
( ) 1
nFV
i
PV