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Suppose 80,000 is due at the end of 4 years with interest at 10%
compounded quarterly. If money is worth 14% compounded quarterly,
what is the value of obligation,
a. Now,
b. At the end of 3 years, and
c. At the end of 6.5 years
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Calculations in the post by the other tutor all are wrong.
I came to bring my corrections.
My corrections are inside.
**1. Calculate the Future Value of the Obligation:**
* **Given:**
* Principal: $80,000
* Interest Rate: 10% per year compounded quarterly (0.10/4 = 0.025 per quarter)
* Number of Periods: 4 years * 4 quarters/year = 16 quarters
* **Formula:**
* Future Value (FV) = Principal * (1 + Interest Rate per Period)^(Number of Periods)
* FV = $80,000 * (1 + 0.025)^16
* FV = $118,760.40 <<<---=== compare with the number $120,756 in the post by the other tutor
**2. Calculate the Present Value of the Obligation:**
* **a. Now:**
* **Discount Rate:** 14% per year compounded quarterly (0.14/4 = 0.035 per quarter)
* **Number of Periods:** 4 years * 4 quarters/year = 16 quarters
* **Formula:**
* Present Value (PV) = Future Value / (1 + Discount Rate per Period)^(Number of Periods)
* PV = $118,760.40 / (1 + 0.035)^16
* PV = 68489.82476 <<<---=== compare with the number $$67,278.31 in the post by the other tutor
* **b. At the end of 3 years:**
* **Future Value at the end of 4 years:** $118,760.40 (calculated above) ! not $120,756, which is wrong
* **Discount Period:** 1 year * 4 quarters/year = 4 quarters
* **Formula:**
* PV = Future Value / (1 + Discount Rate per Period)^(Number of Periods)
* PV = $118,760.40 / (1 + 0.035)^4
* PV = $103,492.83 <<<---=== compare with the number $105,220.41 in the post by the other tutor
* **c. At the end of 6.5 years:**
My comment: The conception of this calculation in the post by the other tutor is wrong from the very beginning.
The right conception is to calculate the Future Value of the obligation in 6.5 years at 10% interest,
and then calculate the Present Value of the obligation at 14% compounded quarterly.
* **Future Value at the end of 6.5 years:** $120,756 (calculated above)
My comment: First, the number 120,756 is wrong;
Second, this number is Future Value at 4 years, not 6.5 years.
So, this conception of the other tutor is wrong in all aspects.
* **Discount Period:** (6.5 - 4) years * 4 quarters/year = 10 quarters
* **Formula:**
* PV = Future Value / (1 + Discount Rate per Period)^(Number of Periods)
* PV = $118,760.40 / (1 + 0.035)^10
* PV = $120,756 / 1.4106
* PV = $85,613.59
My comment: all these reasonings are totally, globally and fatally incorrect
in all possible aspects to such a degree that it is not possible to comment them each separately.
**Therefore:** everything in this post is wrong.
* **a. Value of obligation now:** $67,278.31
* **b. Value of obligation at the end of 3 years:** $105,220.41
* **c. Value of obligation at the end of 6.5 years:** $85,613.59
My comment: everything in this post is wrong.
All numbers of the other tutor are wrong.
All his conception, related to n."c" are wrong.
My conclusion: Everything in the post by the other tutor is wrong, except of my corrections.
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As I see from these numerous posts/solutions produced by the current AI
in the area of Math education/Math help that I saw in the last several days,
it is the contemporary form of global and total deception of people/students.
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