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:

  • Future value
  • Future value of an annuity
  • Present value
  • Present value of an annuity
  • Sinking fund amount
  • Mortgage payment amount


Here are some real-world 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


changes in version 5.1
  • iPad version has new, floating keypad for numerical data entry
  • Source code improvements
changes in version 5.0
  • The iPad version has been extensively rewritten to allow selection of one of the four variables to calculate given each of the other three
  • Also, the iPad version allows decimal terms in months, quarters, or years
  • Custom keypad now is organized in the conventional numerical order
  • Minor GUI changes
changes in version 4.0
  • Rewrite and redesign for iOS 7
  • Expanded number of quarters to 160
  • GUI fixes
changes in version 3.0
  • Major upgrade to include an iPad version
  • Changes and enhancements to workflow, GUI, and functionality
changes in version 2.0
  • Changed the manner of entering and modifying inputs by modifying keypad and code
  • Added ability to move to next or previous data field when editing
  • Added 'Clear' button to zero out all data entries
  • Added 'Mortgage Amortization Schedule' to 'Mortgage Payment' function
  • Increased range of allowable 'Amount' to $10,000,000
  • Improved precision from single to double
  • Numerous GUI changes.

revised: February 11, 2016