SOLUTION: Jonathan obtained his degree and started his own consulting company in January of 2010. At the end of each month he began saving R2 480.00 in his account and requested the bank to

Question 1196378: Jonathan obtained his degree and started his own consulting company in January of 2010. At the end of each month he began saving R2 480.00 in his account and requested the bank to quarterly debit three month sum of his exact savings towards his individual retirement account for a total period of ten years. The retirement account earned interest at 11% per annum, compounded quarterly. The amount that was available to him after ten years in the retirement account is
Found 2 solutions by ElectricPavlov, ikleyn:
Answer by ElectricPavlov(122) (Show Source): You can put this solution on YOUR website!
**1. Calculate Quarterly Deposits:**
* Monthly Savings: R2 480.00
* Quarterly Savings: R2 480.00/month * 3 months/quarter = R7 440.00
**2. Calculate the Number of Quarters:**
* 10 years * 4 quarters/year = 40 quarters
**3. Calculate the Quarterly Interest Rate:**
* Annual Interest Rate: 11%
* Quarterly Interest Rate: 11% / 4 = 2.75%
**4. Calculate the Future Value of the Annuity**
* Use the formula for the future value of an ordinary annuity:
* **FV = P * [(1 + r)^n - 1] / r**
* where:
* FV = Future Value
* P = Quarterly Payment (R7 440.00)
* r = Quarterly Interest Rate (0.0275)
* n = Number of Quarters (40)
* **Calculate:**
* FV = R7 440.00 * [(1 + 0.0275)^40 - 1] / 0.0275
* FV = R7 440.00 * [2.9050 - 1] / 0.0275
* FV = R7 440.00 * 69.2727
* FV = R514 664.79
**Therefore, the amount available to Jonathan after ten years in his retirement account is approximately R514 664.79.**

Answer by ikleyn(52776) (Show Source): You can put this solution on YOUR website!
.
Jonathan obtained his degree and started his own consulting company in January of 2010.
At the end of each month he began saving R2 480.00 in his account and requested the bank
to quarterly debit three month sum of his exact savings towards his individual retirement account
for a total period of ten years. The retirement account earned interest at 11% per annum, compounded quarterly.
The amount that was available to him after ten years in the retirement account is
~~~~~~~~~~~~~~~~~~~~~~~~~

The answer R514,664.79 in the post by @ElectricPavlov is INCORRECT.

The correct answer is R530,235.

The formulas in the post by @ElectricPavlov are correct, but his output final answer is wrong.

It is because they systematically use inadequate calculator or inadequate calculation procedure
for their calculations, which does not provide the necessary precision.

So, if you are looking to get a precise answer for your problems in Finance,
which would be correct at the reference level of accuracy for your answer book,
especially for annuity problems, then @ElectricPavlov is a bad source for such a goal.

As I look at their performance, I clearly see that they do not understand, at all,
what approximate calculations are and which requirements such calculations must satisfy.

So, their level of understanding approximate calculations corresponds to a 5th grade school student,
who makes such calculations for the first time in his life and who never took/got lessons
from an experienced mentor on the subject.

But they stick out their chest like a wheel (or as a monument on a pedestal)
and call themselves "artificial intelligence".

A correct name for such a performance is "charlatanism".

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