The Same $200
One dollar can build wealth or stop a leak. This week you decide which job matters more.
Chapter 6 · Compounding · Assumptions · Opportunity Cost
Discussion 2 gets a classwide recovery window.
Full credit. One-time classwide recovery opportunity.
Why?
D2 had a submission pattern dramatically different from every graded item around it. The gradebook alone does not tell us whether that came from visibility, timing, or communication, so I am not going to pretend I know the cause.
What about the replies?
Your two substantive replies may go to any post already in the D2 thread, including posts from the original window or the recovery window. Replies to already-graded posts count for the student writing the reply.
Your original grade remains in place. No additional work is required.
Before we talk grades, fix the process.
Submission counts so far
Marilyn contributed about $60,000 over 45 years.
What do you think the account was worth at the end?
That is Marilyn Wheeler's answer in Chapter 6.
The finance question is not “Wow, compound interest.”
It is: can you reproduce the number from the information you were given?
An ending balance is an answer to assumptions you may not have been shown.
Use the supplied working assumption: contributions rise linearly from $25/month to $200/month over 45 years. That contributes exactly $60,750.
Move the rate until you can reproduce $437,000. About 8.66% produces roughly $437,055. The chapter never states Marilyn's return, so the rate is an implied assumption, not a reported historical fact.
Run both methods yourself.
The chapter describes a teacher earning $40,000, investing 10%, stated as $333/month, from age 22 to 65 at a 10% return. The published result is about $2.367 million.
Method A · Monthly
$333 deposited monthly with monthly compounding.
Method B · Annual
$4,000 deposited at each year-end with annual compounding.
Monthly vs. book result
This is the “about $486,000” gap used in Discussion 5.
Monthly vs. computed annual method
This is the gap students get when they subtract their two computed methods.
Both gaps are correct because they compare different things.
The book's published $2.367M is rounded and is not identical to the computed annual-method result of about $2.370M.
Now remove three points for inflation.
10% nominal assumption
7% real-return approximation
A projection can be mathematically correct and still answer the wrong question.
You have exactly $200 this month.
Option A: invest it toward long-term wealth. Option B: send it to a $3,000 credit-card balance at 22% APR. No new purchases.
Now calculate the card instead of trusting a check figure.
Payoff time
Total interest
Final payment
Month 1 interest
Month 1 principal
The final payment is smaller than $200.
At the default inputs, month 18 requires about $140.63, not another full $200 payment.
Mathematically, the card is the stronger first target.
The 22% borrowing cost is contractual; Marilyn's implied investment return is not guaranteed. An employer match, emergency-liquidity problem, tax consequence, or penalty can still change the decision.
The Same Two Hundred Dollars
Due Sunday, September 20 at 11:59 PM
Part 1 · Marilyn
Use the $25→$200 monthly linear ramp over 45 years. Solve for the annual return that produces approximately $437,000. Report the rate to two decimals and explain whether it is a stated fact or an implied assumption.
Part 2 · Two calculators
Use the calculator in this lesson. Report both computed ending values. Do not expect their subtraction to equal the Discussion 5 “$486,000” figure. Monthly minus computed annual is about $483,472; monthly minus the book's published $2.367M is about $486,074.
Part 3 · The card
Use the debt calculator in this lesson with $3,000, 22% APR, and $200 monthly payments. Report payoff time, total interest, month-one interest/principal, and the smaller final payment.
Part 4 · Advice
Write a short recommendation: where should the next $200 go and why? Name at least one fact that would change your answer.
Why Are Two Correct Calculators $486,000 Apart?
Due Sunday, September 20 at 11:59 PM
In 175–225 words, explain:
- what assumption creates most of the gap;
- which method better matches the chapter's wording;
- whether either number is appropriate to present as “what you will have” without an inflation caveat; and
- one additional assumption you would require before putting your name on the projection as advice.
Then make two substantive replies. Challenge an assumption, check a calculation, or explain why a different framing would be more defensible.
Build your Week 5 prep note.
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This is what closes this week.
Due Sunday, September 20 at 11:59 PM
Discussion 5 · Why Are Two Correct Calculators $486,000 Apart?
Assignment 2 · The Same Two Hundred Dollars
Also open / not due this week
Discussion 2 recovery window: Due Sunday, September 27 at 11:59 PM.
Chapter 7 stays for next week.
Discussion 6 closes next week.
Assignment 3 closes the following week.
Do the lesson first. Then use your work in D5 and A2.
Finished with the lesson?
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