Six Functions of a $1
'Six Functions of a $1' is a suite of computational routines commonly used in finance,
economics, engineering, and real estate. In any circumstance where the time value of money
is a necessary consideration for investment or return on investment, these routines play a key
role in analysis and decisionmaking.
The six functions are:
 Future value
 Future value of an annuity
 Present value
 Present value of an annuity
 Sinking fund amount
 Mortgage payment amount
examples
Here are some realworld examples that highlight the use of each of the six functions:
Future value:
How much will $1,000 be worth in 15 years if I can get an annual return of
10% per year compounded monthly (for 180 months)?
Answer: $4,453.92
Future value, annuity
I'd like to save for our daughter's college education by investing $5,000 a year
for the next 5 years. I can earn 6% per year on this annual annuity. How much will this plan
achieve?
Answer: $28,185.46
Present value:
I have a chance to purchase an investment that will not produce annual returns
but will return $50,000 to me in 10 years. The seller is driving a hard bargain, but the
investment has relatively little risk. Thus, I will apply a discount rate of just 3.5% per
annum compounded monthly for this opportunity. With these assumptions, what is the maximum
amount I should invest in this opportunity?
Answer: $35,252.36
Present value, annuity:
Our daughter's grandparents are planning to put $25 per month into an existing
college fund. The fund is expected to earn 4.375% per year over the next 15 years (180 months).
Rather than contributing on a monthly basis, her grandparents are able to make a lump sum
contribution today. How much would that lump sum contribution be to produce the same
investment objective?
Answer: $3,295.46
Sinking fund:
I own a small industrial building that has an old HVAC system that I expect
to replace in 5 years at a cost of $5,000. In order to pay for the replacement, I want to
set aside a small amount of money each quarter (20 total quarters) rather than pay the full
amount later. A lender will pay me 8% per annum on the quarterly annuity investment.
What is that quarterly amount?
Answer: $205.78
Mortgage payment:
We'd like to get a $200,000 mortgage to purchase a new home. Our lender is
willing to lend at a 6.5% annual interest rate payable monthly for 30 years (360 months).
On these terms, what will be our monthly mortgage payment?
Answer: $1,264.14
