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annuity

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August 22, 2025 Score: 1 Rep: 868 Quality: Medium Completeness: 20%

The car is "worth" $40,000, as that's the cash price you could buy it for.

Paying $45,000 in monthly payments over 4 years is an APR of 3.05% (I used an online calculator to get that number.)

There are three investments you could make with your money: money fund at 2%, forego car loan at 3.05%, and pay down credit card bill at 15%.

Looking at it that way the choice is pretty clear.

(It's an oversimplification, of course, as there is value to having cash on hand for unexpected expenses, there may be tax implications, and there is value to not having fixed financial obligations if you have variable income, but from a strict cash income perspective the best investment of the three is paying down credit card debt and the worst investment is the 2% mutual fund.)

August 16, 2025 Score: 0 Rep: 9,769 Quality: Low Completeness: 10%

In either case you finance the $40,000. The only difference is that in the first case you don't pay the interest out of pocket, but it's lost income. However that makes no difference whatsoever: you have to pay one way or another.

So the only relevant difference here is the interest rate, 2% vs 15%, otherwise the math is the same. Turns out, the break even point is about 3%: if you can finance for less than that: go for it.

August 24, 2025 Score: 0 Rep: 1,306 Quality: Low Completeness: 20%

I think the phrasing of option b) is unclear. What they are actually comparing is pay the $40,000 with the credit card right now (and then pay 15% annual interest on it) versus pay $937.50 per month with the credit card (and then pay 15% annual interest every month on the total amount so far charged on the credit card). If you then compare how much credit card debt you have after 4 years, paying monthly installments is better.

The numbers they are comparing is the debt in 4 years rated backwards to today with 15% annual interest rate. Then the $40,000 paid in cash today is exactly $40,000 today but the debt on the credit card with monthly payments looks much smaller.

August 16, 2025 Score: -1 Rep: 29 Quality: Low Completeness: 40%

Upon further reflection, answering my own question:

  1. When comparing the alternative deals in this problem, we are talking only about PV (present value). We explicitly do not care about future value or the total amount of money we will ultimately pay in any of the cases.

  2. Whether the interest rate is thought of as a yield or as a cost is irrelevant. The whole point of PV is that whichever side of the transaction we are on, whether we are the credit card company or the individual, we all agree on the PV. So we can just forget about the directionality of the payments and just focus on comparing the financed PV to the cash PV.

So just to be clear, the solutions provided are indeed correct, it was only my intuition/understanding that was wrong.