I apologize for not answering sooner, but I find this question a bit difficult to address due to the complexity of formulas we can encounter. I know the one you documented is not the most complex one we might encounter, but I was not sure if that was your actual problem or if it was intended as a simple example. I have seen a variety of other things which have often thrown me for a loop.

For example, take this set of rules:

Minimum Fee is $23.50 up to $500
$501 - $2,000 = $3.05 per 100 unit increment
$2,001 - $25,000 = $14.00 per 1000 unit increment over $2,000
$25,001 - $50,000 = $10.10 per 1000 unit increment over $25,000
$50,001 - $100,000 = $7.00 per 1000 unit increment over $50,000
$100,001 - $500,000 = $5.60 per 1000 unit increment over $100,000
$500,001 - $1,000,000 = $4.75 per 1000 unit increment over $500,000
$1,000,001 - $9,999,000 = $3.65 per 1000 unit increment over $1,000,000
$10,000,001 and up = $3.65 per 1000 unit increment over $10,000,000

It does not look too different from yours except that there is an increment of something other than a single unit. In other words for the $501 to $2,000 range, $501 to $600 would all get the same additional $3.05 incremental charge. Another dollar would actually double this because it jumps to the next increment. Like your example, each range builds on the prior range. Assuming that these amounts are in colums A through F:

i   Low                 High    Fee     Base Fee    Per
0             1          500              23.50 
1           501        2,000    $3.05                100
2         2,001       25,000   $23.50               1000
3        25,001       50,000   $10.10               1000
4        50,001      100,000    $7.00               1000
5       100,001      500,000    $5.60               1000
6       500,001    1,000,000    $4.75               1000
7     1,000,001    9,999,999    $3.65               1000
8    10,000,000                 $3.65               1000

Note also that the rate declines as the amounts increase whereas yours appears to increase.

What I did with this is create a maximum value in Column H as follows:

i   Max
0   =E3
1   =INT((C4-C3)/F4)*D4
2   =INT((C5-C4)/F5)*D5
3   =INT((C6-C5)/F6)*D6
4   =INT((C7-C6)/F7)*D7
5   =INT((C8-C7)/F8)*D8
6   =INT((C9-C8)/F9)*D9
7   =INT((C10-C9)/F10)*D10
8   

The first one, where i is zero, is simply the base fee. The others are computed and copied. There is no maximum for the last row. I did not really think I needed this column but it made it easier to devise the formulas.

Assuming that I put an amount to evaluate in Cell I2, it will be evaluated as follows where the formula in row 3 (where i=0) is the set fee but all others are basically a copied formula:

i   4,950
0   =IF(I$2>=$B3,$H3,0)
1   =IF(I$2>=$B4,IF($H4="",INT((I$2-$C3)/$F4)*$D4,MIN($H4,INT((I$2-$C3)/$F4)*$D4)),0)
2   =IF(I$2>=$B5,IF($H5="",INT((I$2-$C4)/$F5)*$D5,MIN($H5,INT((I$2-$C4)/$F5)*$D5)),0)
3   =IF(I$2>=$B6,IF($H6="",INT((I$2-$C5)/$F6)*$D6,MIN($H6,INT((I$2-$C5)/$F6)*$D6)),0)
4   =IF(I$2>=$B7,IF($H7="",INT((I$2-$C6)/$F7)*$D7,MIN($H7,INT((I$2-$C6)/$F7)*$D7)),0)
5   =IF(I$2>=$B8,IF($H8="",INT((I$2-$C7)/$F8)*$D8,MIN($H8,INT((I$2-$C7)/$F8)*$D8)),0)
6   =IF(I$2>=$B9,IF($H9="",INT((I$2-$C8)/$F9)*$D9,MIN($H9,INT((I$2-$C8)/$F9)*$D9)),0)
7   =IF(I$2>=$B10,IF($H10="",INT((I$2-$C9)/$F10)*$D10,MIN($H10,INT((I$2-$C9)/$F10)*$D10)),0)
8   =IF(I$2>=$B11,IF($H11="",INT((I$2-$C10)/$F11)*$D11,MIN($H11,INT((I$2-$C10)/$F11)*$D11)),0)

The Fee for this is the sum of all of the rows (labeled i, 0 through 8 above). in this example, it would be 23.50 plus 45.75 plus 28.00 for a total of 97.25.

Not too bad. How about a set like this:

No fee if $1,000 or less
$1,001 - $5,000 = $80.00 + 3% of excess over $1,000.00 per 100 unit increment
$5,001 - $10,000 = $250.00 + 2% of excess over $5,000.00 per 500 unit increment
$10,001 - $25,000 = $350.00 + 1% of excess over $10,000.00 per 1000 unit increment
$25,001 and Over = $520.00 + 3/4% of excess over $25,000.00 per 1000 unit increment

In your formula, the initial flat amount never changes and once you've computed the amount for that range, other ranges build upon it. Here, there are steps. For example at $1,000 the fee is zero, but at $1,001, it jumps to $80 as if there were an $80 fee for the first 1000. Without boring you with the entire table, Here is the formula for computing the range from 5,001 to 10,000 assuming that G2 contains the amount to use and Row 5 colums A through E are the following:

Low     High        Rate      Minimum   Increment
 5,001   10,000     2.00%        250         500 

=($D5+$C5*INT(($G$2-($A5-1))/$E5)*$E5)*($G$2>=$A5)*OR($B5="",$G$2<=$B5)

The formula simply looks at the current row and does the computation if the amount in G2 falls within the range from Column A to Column B.

A simplification of all of the above comes when each range cumulatively builds on the prior ranges AND the rate of payment is always increasing, like the U.S. Tax Tables:

    Over    Not Over        
      0       9,525     10% of taxable income
  9,525      38,700     $952.50 plus 12% of the excess over $9,525
 38,700      82,500     $4,453.50 plus 22% of the excess over $38,700
 82,500     157,500     $14,089.50 plus 24% of the excess over $82,500
157,500     200,000     $32,089.50 plus 32% of the excess over $157,500
200,000     500,000     $45,689.50 plus 35% of the excess over $200,000
500,000                 $150,689.50 plus 37% of the excess over $500,000

Here, we can use something referred to as the "deskpad method" to shortcut the computation

Assuming that the amount to be evaluated is in G1 and these are in column A through C starting in Row 1:

Over    Not Over    Rate
      0   9,525     10.0%
  9,525  38,700     12.0%
 38,700  82,500     22.0%
 82,500 157,500     24.0%
157,500 200,000     32.0%
200,000 500,000     35.0%
500,000             37.0%

We compute the amount based on G1 as follows:

=ROUND(SUMPRODUCT($C$2:$C$8-$C$1:$C$7,$G$1-$A$2:$A$8,N($G$1>$A$2:$A$8)),0)

Note: this is not entered as an array formula.

How does this relate to your question. If the need is as simple as you stated (in other words, the rate is always increasing and we do not have any "steps" in the reimbursement, we can compute it similarly to the U.S. Tax computation.

I created these values in columns A through D starting in row 1:

Over    Not Over        
  0      20     £-      Flat Amount of £10.00
 20      50     £0.50   £10.00 plus £.50 per mile over 20 miles
 50     100     £1.00   £25.00 plus £1.00 per mile over 50 miles
100             £1.50   £75.00 plus £1.50 per mile over 100 miles

where column D is just descriptive. I put the £10.00 flat fee in Cell E1.

Assuming that G1 contains the number of miles, we would compute the reimbursement as:

=$E$1+ROUND(SUMPRODUCT($C$2:$C$5-$C$1:$C$4,$G$1-$A$2:$A$5,N($G$1>$A$2:$A$5)),2))

For example, when G1 is 52 miles, the computation is £27.00

Note: this is not entered as an array formula.

So, if this is the situation, what you would need is a place to house Columns A through C, a place to house the flat amount and a formula similar to what I provided to compute the reimbursement based on the cell housing the number of miles.

Please note that all the earlier items indicate that this formula will not be so simple if the rate is stepped or the rate declines or if the incremental unit is something other than 1 mile.

I hope that some of this makes sense. Good luck.