What is the total amount

Question

John will be paying R 159 vat included the agreement is for 36 moths which will increase annually by 10%

Answer 1

It’s assumed that the accumulated VAT after 36 months is R159 and that we need to find the original purchase price. This question could be interpreted in two ways: simple VAT and compound VAT.

SIMPLE VAT

At 10% per year, that would be 30% after 3 years, so R159 is equivalent to 30%, making the purchase price 159/0.3=$530. After the first year the VAT would be 10% of R530 which is R53. The same amount of VAT is added each year, so the total amount would be 3×53=R159 after 3 years.

COMPOUND VAT

If the original purchase price was x, then after VAT on the first year, the value would rise to 1.1x. VAT on this comes to 1.1²x=1.21x for the second year and 1.1³x=1.331x for the third year. The total VAT is 1.331x-x=0.331x=159, so x=159/0.331=R480.36. After the first year the VAT would be R48.036 or about R48.04. This is added to the original purchase price, making about R528.40 for the second year. 10% of this is R52.84 approx, making R581.24 for the second  year. 10% of this is R58.12, added to R581.24=R639.36, so total VAT is 639.36-480.36=R159.

(A third way to interpret the question would be simply to multiply 159 (assumed to be the annual VAT) by 3 to give the total VAT after 36 months=R477, but this doesn’t include the 10% factor. Therefore, it would be compound VAT, rising to 159(1.1)³=R211.63 in total after 36 months.)

 

Comments

Or it can be recurring deposit + compound interest.

Like depositing R 159  each month. and calculate the interest.

then the formula to be used should be:

Interest = P * n(n+1)/2 * r/12

And Amount = P*n + Interest.

And we have to do this for 3 different years, updating the interest.

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It’s not easy to tell from the question what the intention is. The question doesn't qualify what total amount means: total amount paid or total VAT.

I thought perhaps it was a matter of working out the value of the goods or services knowing the first year VAT was R159, then increasing the VAT based on annually compounded interest for 36 months. Anyway, I guess the user will decide which option is most appropriate.