I have written a few Financial Calculators over the past couple of weeks, and one approach I've found extremely useful is Approximation and Guesswork.
So I figured, why not share the approach with the forum,
Rather than re-inventing a load of different functions to find missing values, I take one formula and turn it around (rather similar to the Goal Seek in Excel).
Here's how my version of approximation works:
(This is the old Jackson Structured Programming diagram - still relevant today
The beauty of the Approximation approach is that you can find any missing parameter to any calculation with no prior knowledge of the actual calculation itself!
And it's fast.
In this example, I have used a low value of 0 years, a high value of 100 years, so the mid is 50 years.
Each loop halves the difference between the low and mid, or the mid and high, so in a very small number of iterations, you can get from 100 years down to single digits very quickly.:
After only 5 loops, we are already very close to the required answer. The example below takes about 20 loops to get to the final result. Sometimes, I will build in a 'tolerance' amount, which can significantly reduce the iterations, but when dealing with calculators, it's more important to be accurate, so I decide on a tolerance on a case-by-case basis.
In the example below, I've set up a simple Present Value (PV) function. It takes three parameters - the Future Fund Value, the Interest Rate and the Term, and returns the present value of the funds. But the approach can be applied to any complex calculation you can think of.
Here's the code:
In my Approximation routine, I am attempting to find the Term (I expect to get an answer of 5 years in this case)
The "Log" statement will give you a good idea of what's happening in the background.
I first came across the Approximation approach wayyyyyy back in 1979, when I was writing code using punch cards in Assembler (Search for punch cards - it's worth it
So I figured, why not share the approach with the forum,
- A) to hopefully inform and
- B) to see if anyone else has any other intriguing approaches.
Rather than re-inventing a load of different functions to find missing values, I take one formula and turn it around (rather similar to the Goal Seek in Excel).
Here's how my version of approximation works:
(This is the old Jackson Structured Programming diagram - still relevant today
The beauty of the Approximation approach is that you can find any missing parameter to any calculation with no prior knowledge of the actual calculation itself!
And it's fast.
In this example, I have used a low value of 0 years, a high value of 100 years, so the mid is 50 years.
Each loop halves the difference between the low and mid, or the mid and high, so in a very small number of iterations, you can get from 100 years down to single digits very quickly.:
| Iteration | Low | Mid | High |
| 1 | 0 | 50 | 100 |
| 2 | 0 | 25 | 50 |
| 3 | 0 | 12.5 | 25 |
| 4 | 0 | 6.75 | 12.5 |
| 5 | 0 | 3.87 | 6.75 |
After only 5 loops, we are already very close to the required answer. The example below takes about 20 loops to get to the final result. Sometimes, I will build in a 'tolerance' amount, which can significantly reduce the iterations, but when dealing with calculators, it's more important to be accurate, so I decide on a tolerance on a case-by-case basis.
In the example below, I've set up a simple Present Value (PV) function. It takes three parameters - the Future Fund Value, the Interest Rate and the Term, and returns the present value of the funds. But the approach can be applied to any complex calculation you can think of.
Here's the code:
Present Value Calculation:
Sub PV(FV As Double, rate As Double, term As Double) As Double
Return(FV * (1 / (Power((1+rate),term))))
End SubIn my Approximation routine, I am attempting to find the Term (I expect to get an answer of 5 years in this case)
Approximation:
Sub Approximate
Dim Mid As Double = 50 ' Mid value is the value we will use to calculate the PV (When the Target result is reached, the Mid value ifs the one we want
Dim Low As Double = 0 ' Used to control how Mid value is calculated
Dim High As Double = 100 ' also used to control how the mid value is calculated
Dim Target As Double ' The target value we want to achieve
Dim myPV As Double = 0 ' Holds the result from the PV calculation
Dim myFV As Double = 5000 ' The Future Value Amount
Dim myRate As Double = .03 ' The Annual Interest Rate
Target = (PV(myFV,.03,5)) ' TARGET IS SET UP HERE ONLY TO AID THE EXAMPLE.
Log("Target: " & Target)
Do While (Round2(myPV,2)<>Round2(Target,2))
myPV = PV(myFV, myRate, Mid)
Log("Low: " & Round2(Low,2) & "; Mid: " & Round2(Mid,2) & "; High: " & Round2(High,2) & " - Result=" & Round2(myPV,2))
If Round2(myPV,2) > Target Then
Low = Mid
else if Round2(myPV,2) < Target Then
High = Mid
End If
Mid = (Low + High) / 2
Loop
xui.MsgboxAsync(Round2(Mid,2),"Result")
End SubThe "Log" statement will give you a good idea of what's happening in the background.
I first came across the Approximation approach wayyyyyy back in 1979, when I was writing code using punch cards in Assembler (Search for punch cards - it's worth it