26) Missing 28) Missing 30) Missing MATH 034 Formulas 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 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 ) / (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 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 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) 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 an/i = present value annuity factor Inte.

1. 26) Missing
28) Missing
30) Missing

2. MATH 034 Formulas
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

3. M = maturity value
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

4. 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
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

5. FV = future value
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

6. 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
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)

7. 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

8. 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
i
n
i
i
a
n
in

9. )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

10. 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

11. 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

12. 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

13. 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

14. 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

15. Cost-Revenue Analysis
P = R – C
P = profit function
R = revenue function
C= cost function
1/
( ) 1
nFV
i
PV
Math 034 First Letter of Last Name
Homework #5 Full Name ___________________________
Due Wednesday 10/14/15 Section
_____________________________
1. (Section 4.1) Andrew deposits $500 from each of his monthly
paychecks into a 401(k) savings plan at work. He

16. will keep this up for the next 37 years, at which time he plans to
retire, hopefully having accumulated a large
balance in his account.
a. Is the value of the account when he retires a present value or
a future value?
b. Is this an ordinary annuity or an annuity due?
2. (Section 4.1) Jennifer borrowed $225,000 to buy a house. To
pay off this mortgage loan, she agreed to make
monthly payments at the beginning of each billing cycle.
a. Is the amount she borrowed a present value or future value?
b. Is this an ordinary annuity or an annuity due?
3. (Section 4.2) Find the future value annuity factor for a term
of 29 years with an interest rate of 6.75%
compounded annually.
4. (Section 4.2) Suppose that Ryan deposits $350 each month
for 25 years into an account paying 5 3/8% interest.
What will the future value of the account be?
5. (Section 4.2) How much total interest did Ryan earn in
problem #4?
6. (Section 4.2) Tiffany plans to deposit $4,500 at the beginning
of each year into a retirement savings account.
Assuming that she continues these deposits, and that her
account earns 7.5% compounded annually, how much

17. money will she have accumulated after 36 years?
7. (Section 4.3) Patrick plans to start graduate school in 4 years
after obtaining an undergraduate degree. He
determines that he will need to save up $60,000 in 4 years. He
decides that he will make weekly deposits into
an investment account. How much money will he need to
deposit each week, assuming that his savings earn
3.25% interest?
8. (Section 4.3) Assume that you are 24 years old and hope to
be able to retire 43 years from now, at age 67. To
ensure that you can do so comfortably, you decide to start
making deposits into an investment account which
you assume can earn an average of 6% interest. The deposits
will be automatically deducted from your biweekly
paycheck. To get some sense of how large your deposits should
be, you set a goal of having $850,000 in your
retirement account. Determine how much you should deduct
from each paycheck to reach your goal.
9. (Section 4.3) Determine the total amount of interest you will
be earning in problem #8.
10. (Section 4.4) Nick just graduated from college and is
thinking about buying a car. He determines that he can
afford monthly loan payments of $400, and that he would be
taking out a 5-year loan with an interest rate of
4.9%. What is the most he can afford to pay for a car?

18. 11. (Section 4.4) Sean and Jillian are buying a house and will
need to take out a $200,000 mortgage loan. They plan
to take out a standard 30-year mortgage loan with an interest
rate of 3 7/8%. Find their monthly payment.
12. (Section 4.4) Find the total amount of interest Sean and
Jillian will pay for their 30 year mortgage in problem
#11.