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 decision-making.
The six functions are:
Here are some real-world examples that highlight the use of each of the six functions:
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)?
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
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?
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
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?
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?
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revised: November 28, 2021