


(F/P,
i, n): Single payment compound amount factor 

E_FP(interest rate
per period, number of periods) 

At age 5 you
were left $10,000 from the fortune of a favorite aunt.
Your parents put the money in a trust fund earning 10%
interest. You are now 25 years old and may draw from the
trust fund. How much do you have? 



You can withdraw
$62,275 from the bank. 



(P/F,
i, n): Single payment present worth factor 

E_PF(interest rate
per period, number of periods) 

You win the lottery
and the government promises to pay you $1,000,000 in ten
years. Your minimum acceptable rate of return on investments
is 10%. What is the prize worth to you now? 



With a minimum return
of 10%, you should accept no less than $385,543.29. 



(A/F,
i, n): Sinking Fund factor 

E_AF(interest rate
per period, number of periods) 

You are 20 years
old and just got married. Your spouse and you agree that
you want to retire at age 60 with $1,000,000. How much
do you have to put away each year if you earn 10% on your
investments. 



You must put away
$2259.41 per year, or less than $200 per month to be a millionaire
by the time you are 60 years old. 



(F/A,
i, n): Uniform Series Compound Amount factor 

E_FA(interest rate
per period, number of periods) 

You are a parent.
Your daughter starts college in 18 years. If you put away
$100 each month for 18 years, how much will you have when
she is ready to begin college? The CD's you invest in return
6% per year compounded monthly.
Since the payments are monthly, we use a monthly interest
rate in the factor and express the number of periods
in months. 



The deposits will
grow to $38,735. 



(A/P,
i, n): Capital Recovery Factor 

E_AP(interest rate
per period, number of periods) 

You finally have
a job after 4 years of college. To escape the high rent
of the Austin area you buy a house for $100,000. You finance
the full amount with a 30 year mortgage. The interest rate
is 9% a year, and your payments are monthly. What are the
total of all payments if you make all payments as scheduled?
Since the payments are monthly, we use a monthly interest
rate in the factor and express the number of periods
in months. 



The total you will
pay is almost three times the amount of the loan. The interest
is the difference between the total payments and the loan
amount, $189,664. 



(P/A,
i, n): Uniform Series Present Worth Factor 

E_PA(interest rate
per period, number of periods) 

You can afford
$300 a month to purchase a car. If the interest rate is
6% a year and the loan is for 60 months, how much can you
finance?
Since the payments are monthly, we use a monthly interest
rate in the factor and express the number of periods
in months. 



The present value
of the loan payments is the amount that you can borrow. 



(P/G,
i, n): Arithmetic Gradient Present Worth Factor 

E_PG(interest rate
per period, number of periods) 

You are a freshman
in college and you just paid $1000 for tuition and fees
for the University. Assuming the cost goes up by $100 per
semester for the remaining 7 semesters of your education,
how much must you have in the bank right now to cover the
remaining charges? Assume your investments earn 3% every
six months.
Since the payments are twice a year, the interest rate
is the six month rate and the number of periods is in
semester intervals. Note than the gradient series is
ontopof a uniform series, so the present worth formula
has two terms. 



You must have $8648.79
in the bank to pay your remaining tuition bi. 



(A/G,
i, n): Arithmetic Gradient to Uniform Series Factor 

E_AG(interest rate
per period, number of periods) 

You are a freshman
in college and you just paid $1000 for tuition and fees
for the University. Assume the cost goes up by $100 per
semester for the remaining 7 semesters of your education.
Your parents will send you a fixed amount every semester
to cover your fees. What payment every semester will provide
your tuition through your college career. Assume your investments
earn 3% every six months. 



Assuming you invest
the excess, a uniform payment of $1388.19 will take care
of your tuition for the remaining 7 semesters. 



(P/G,
i, g, n): Geometric Series Present Worth Factor 

E_PGeo(interest rate
per period, percentage increase per period, number of periods) 

What is the amount
of 10 equal annual deposits that can provide five annual
withdrawals, when a first withdrawal of $1,000 is made
at the end of year 11, and subsequent withdrawals increase
at the rate of 6% per year over the previous year's if
the interest rate is 8%, compounded annually? 



An annual payment
of $307.96 for ten years will provide the amount necessary
for the withdrawals. 