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.
Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's how to calculate the net value of the deposit:
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 * 1.0226
Future Value ≈ 102,260 pesos
4. **Calculate the tax amount:**
The tax rate is 21%, so the tax amount is:
Tax = Future Value * tax rate
Tax = 102,260 * 0.21
Tax ≈ 21,474.60 pesos
5. **Calculate the net value after tax:**
Net Value = Future Value - Tax
Net Value = 102,260 - 21,474.60
Net Value ≈ 80,785.40 pesos
Therefore, the net value of the deposit after 3 quarters, after the 21% tax is applied, is approximately $\boxed{80,785.40}$ pesos.
Answer by ikleyn(52786)  (Show Source):
You can put this solution on YOUR website! .
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.
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.
Solved correctly, to get perfectly correct answer.
--------------------------------
The rule of such calculations is: do not make intermediate rounding.
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
>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
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