Sheldon Wang

Sheldon Wang

Staff Engineer · Agentic Systems & AI Infra

🚗 Car Payment Is The Biggest Reason That Keeps You Poor 💸

Published:

How much money you can lose if you buy a 70k car now. We can do a simple math.

🚗 Make the Purchase

Firstly, let’s calculate how much we lost in interest rate because of the loan. 💸

Fees before car out of door

Assuming dealer has some fees around 1k, and sales tax 8% = 5.6k, some additional fees like warranty, window tint etc 2k. The total cost is 70k + 1k + 5.6k + 2k = 78.6k

Assuming 10k downpayment, 8% APR interest rate, 60 month payments

8% interest rate for 60-month car payments

\[P = $68,600\] \[r = \frac{0.08}{12}\] \[n = 72\]

Now, let’s calculate the monthly payment:

\[r = \frac{0.08}{12} = 0.006666...\] \[M = 68600 \times \frac{0.006666... \times (1 + 0.006666...)^{72}}{(1 + 0.006666...)^{72} - 1}\] \[M = 68600 \times \frac{0.006666... \times (1.006666...)^{72}}{(1.006666...)^{72} - 1}\] \[M ≈ 68600 \times \frac{0.006666... \times 1.776129}{1.776129 - 1}\] \[M ≈ 68600 \times \frac{0.011840}{0.776129}\] \[M ≈ 68600 \times 0.015234\] \[M ≈ 1044.95\]

So, with no down payment, the approximate monthly payment for a $68,600 car with an 8% APR over a 6-year term would be approximately $1,044.95, totaling $75,417.60 acoss the 6 years. With 10k downpayment, we spent $85,417.60 so far.

Car is a Depreciating Asset! 📉

Secondly, let’s also take the car depreciation value into our consideration. 🚗

National average car depreciation rate

The depreciation of a car over time can vary based on factors like make, model, condition, and mileage. However, as an approximation, the national average depreciation rate for a car after 6 years is estimated to be around 50-60% of its original value.

Let’s take the midpoint of this range for our calculation, assuming a depreciation rate of 55%.

If the car’s original price is $70,000, after 6 years, its depreciated value would be:

\[Depreciated\,Value = Original\,Price \times (1 - Depreciation\,Rate)\] \[Depreciated\,Value = $70,000 \times (1 - 0.55)\] \[Depreciated\,Value = $70,000 \times 0.45\] \[Depreciated\,Value = $31,500\]

Losing

Now we can know the total lost value is:

\[Total\,Lost\,Value = $85,417.60 - 31,500\] \[Total\,Lost\,Value = $54,417.60\]

What if We Invest Instead? 💰

Thirdly, let’s calculate how much we will lose in a very conservative investment rate with 8% in S&P 500 index fund annual return rate. 📈

Calculation:

Future Value of Initial Investment: \(FV_{\text{initial}} = 10,000 \times (1 + \frac{0.08}{12})^{72}\)

\[FV_{\text{initial}} ≈ 10,000 \times (1.00667)^{72} ≈ 10,000 \times 1.717\] \[FV_{\text{initial}} ≈ 17,170\]

Future Value of Monthly Investments: \(FV_{\text{annuity}} = 1044.95 \times \frac{(1 + \frac{0.08}{12})^{72} - 1}{\frac{0.08}{12}}\)

\[FV_{\text{annuity}} ≈ 1044.95 \times \frac{(1.00667)^{72} - 1}{0.00667} ≈ 1044.95 \times 94.506\] \[FV_{\text{annuity}} ≈ 98,978.16\]

Total Future Value: \(FV_{\text{total}} = FV_{\text{initial}} + FV_{\text{annuity}}\)

\[FV_{\text{total}} ≈ 17,170 + 98,978.16\] \[FV_{\text{total}} ≈ 116,148.16\]

So, the total future value is approximately $116,148.16.

Profit

The profit is $46,148.16.

The Final True Losing Value 😱

On a given car with 70k price tag, we are looking at:

\[Difference = $54.4k + $46.1k = $100.5k\] \[Investment Rate = -$100.5k / $70k = -143%\]

In other words, we are losing 100.5k truely taking the opportunity cost into consideration, that is -143% in investment return rate. If you think my math is mathing, please consider sharing to make the people around you making better financial decisions!

Demo