Question 1186537
.
A bank earns 3% interest per annum compounded monthly for an initial savings deposit of 100,000 pesos. 
Find the net value of the deposit after 3 quarters if the earning is subjected to a 21% tax.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~



        In the post by @CPhill, the chart flow (the sequence) of calculations is correct,

        but the precision is not enough, so his resulting value (his answer) is not absolutely correct.


        I will repeat here all his steps, using Excel as my calculator, 

        and will get another answer with quite visible/significant difference.



<pre>
1. **Calculate the interest rate per month:**
   The annual interest rate is 3%, so the monthly interest rate is 3% / 12 = 0.25% or 0.0025 as a decimal.

2. **Calculate the number of months in 3 quarters:**
   There are 3 months in a quarter, so 3 quarters is equal to 3 * 3 = 9 months.

3. **Calculate the future value of the deposit before tax:**
   We use the formula for compound interest:
   Future Value = Principal * (1 + interest rate)^number of periods
   Future Value = 100,000 * (1 + 0.0025)^9
   Future Value = 100,000 * (1.0025)^9
   Future Value ≈ 100,000 * 1.022726317  <<<---===  it is first place, where my number is different from @CPhill.
   Future Value ≈ 102,272.63 pesos       <<<---===  @CPhill gives here 102,260 pesos. 

4. **Calculate the tax amount:**
   The tax rate is 21%, so the tax amount is:
   Tax = Future Value * tax rate
   Tax = 102,272.63 * 0.21
   Tax ≈ 21,477.25 pesos

5. **Calculate the net value after tax:**
   Net Value = Future Value - Tax
   Net Value = 102,272.63 - 21,477.25
   Net Value ≈ 80,795.38 pesos

Therefore, the net value of the deposit after 3 quarters, after the 21% tax is applied, is 80,795.38 pesos.

Compare here with the answer by 80,785.40 by @CPhill.


The difference appeared, because @CPhill in his calculations makes intermediate rounding, losing precision.
</pre>

Solved correctly, to get perfectly correct answer.


--------------------------------


The rule of such calculations is: &nbsp;&nbsp;do not make intermediate rounding.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Make the final rounding at the end, ONLY.



At this forum, I just noticed and pointed out a similar error/deficiency in the post by @CPhill under the link


<A HREF=https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.1190651.html
>https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.1190651.html
</A>

https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.1190651.html