Hi,

I run across this a lot at work and I haven't been able to figure it out.

A customer pays a total of 15 dollars for an item. Sales tax is 10%. What was the original price of the item before taxes. I know the formula is as follows and using all of my high school alg. Has only gotten me so far.

n+(n*.10)=15

I can't figure out what n would be... Any help is appreciated.

Thanks.

Your first problem is your trying to use a difficult method to answer such an easy question.
Your formula to figure out this question is:

15.00 / 1.10 = 13.64
Therefore, if the customer paid 15.00 total it would have cost 13.64 before a 10 percent tax.

difficult method? I do not see any difficult method in his formula. In fact if you notice it is exactly what you did!

n + (n * 0.10) = 15
n + 0.10n = 15
1.1n = 15
n = 13.64

Finish answer please and tell where you get 1.1 for us math dummies

Here's another problem. I have a tariff the electricity board pay on my solar panel. The tariff is 0.413 cents/kWh. It rises by 2.4% each year. The system generates 1785 kWh in the first year, going down by 0.5% each year (as its cells decay). I want one formula that works out the total cumulative income after n years. People give me different answers to this and they are usually wrong as I've made a spreadsheet up that adds them up laboriously!

For starters, a little tip... your question has better odds of garnering attention if you'll start a new thread for it.

Your tariff problem plays out as a sum of a geometric progression, where the sum S_n of the first n terms is given by

S_n \ = \ \frac{a(r^n-1)}{r-1}

... where your initial term a is the product (1,785)(0.413) and the common ratio r is the product (0.995)(1.024).

Give that one a spin and check it against your spreadsheet results for various test values of n years.

I tried it but it doesn't work. Perhaps some real numbers might help.

To recap: tariff = 0.413. The amount being produced is 1785 kWh per year. The rate changes by 2.4% per year. The panels diminish in power by 0.5%.

The first year no rises occur. It's just a straight multiplication. Then from year two, we see the changes.

There must be a quick way to enter n into a formula and work out the cumulative SUM of 10 years, 20 years and 25 years. See below for the 25th year.

£737.21
£751.12
£765.30
£779.75
£794.48
£809.48
£824.76
£840.33
£856.19
£872.36
£888.83
£905.61
£922.71
£940.13
£957.88
£975.96
£994.39
£1,013.16
£1,032.29
£1,051.78
£1,071.64
£1,091.87
£1,112.49
£1,133.49
£1,154.89
Cumulative total after n=25 years =23,278.11

Yes, and the result of the formula I gave, for n = 25, is

\frac{737.205(1.01888^{25}-1)}{1.01888-1} = 23,278.11

You'll find it also agrees with your schedule for any n.

Remember, the values for a and for r, as shown here, do not change. Just adjust the exponent to agree with the number of years, and you're good to go.

Ah, now I see it. So the trick is to multiply the ratios together. (1+d)(1-i) to give r. Then, as long as one knows 'a' the first term, you plug this into the formula. You are one smart guy. Thanks.

Glad to help, 3235... and I appreciate it. Take care,

Here is something else I would like to work out that is related to the above. Okay this is more complex, and I can do it on a spreadsheet, but I wonder if there's anyway to incorporate it into the above formulae? You may know that it is usual for accountants to apply 'discount rates' which are variable, usually from tables. As a rough approximation, the formula 1/(1+r)^n is used where r is usually 3.5/100 (3.5%). This is called the discount rate and if you start pumping in year numbers you notice that each year the discount rate thus changes: 0.9950, 0.9335, 0.9019 etc... (year n=1, 2, 3 and so on). These figures would normally be multiplied by the total earnings the system makes each year. Now in our cumulative sums above r is the product of two fixed values (rise of 2.4% and the fall of 0.5%) unlike this discount rate. I wonder if it is possible to work this into a 'predictive' formula based on geometric progression cumulative sum formulas like above? See Net Present Value.