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Investment-01-Investing or Mortgage-01-Comparative Analysis

🔎 Intro

In this blog post, I’ll run a quick analysis on the common dilemma of whether to invest extra money or pay off your mortgage early. In the current high interest situtaion, this has become a question that stays in my mind.

When deciding whether to invest in the stock market or pay off your mortgage, it’s essential to weigh the potential returns against the guaranteed savings. Based on some current interest rates in UK and the annual stocks return rate of US market in recent years, let’s use some imaginary assumptions and break down the numbers for both options over a 2-year and 5-year period to quickly compare the outcomes.

Assumptions

  • Monthly Cash Available: £2,000
  • Monthly Mortgage Payment: £2,000
  • Mortgage Interest Rate: 5.8%
  • Investment Return Rate: 7% - 10% per year
  • Investment Period: 2 years and 5 years

Investing in Stocks

2-Year Scenario

Using the Future Value formula, we can calculate the future value of the investment after 2 years:

FV = P * (((1 + r/n)**(n*t) - 1) / (r/n))

FV = £2,000 * (((1 + 0.07/12)**(12*2) - 1) / (0.07/12)) &approx £51,362

FV = £2,000 * (((1 + 0.10/12)**(12*2) - 1) / (0.10/12)) &approx £52,894

Where:
P: Monthly investment amount
r: Annual interest rate (expressed as a decimal, e.g., 0.07 for 7%)
n: Number of compounding periods per year
t: Number of years

5-Year Scenario

Similarly, we can calculate the future value of the investment after 5 years:

FV = £2,000 * (((1 + 0.07/12)**(12*5) - 1) / (0.07/12)) &approx £143,186

FV = £2,000 * (((1 + 0.10/12)**(12*5) - 1) / (0.10/12)) &approx £154,875

Paying off Mortgage

2-Year Scenario

Using the modified Future Value formula, we can calculate the mortgage reduction for the future value of an annuity due after 2 years:

FV = P * (((1 + r/n)**(n*t) - 1) / (r/n)) * (1 + r/n)

FV = £2,000 * (((1 + 0.058/12)**(12*2) - 1) / (0.058/12)) * (1 + 0.058/12) &approx £51,617

5-Year Scenario

Similarly, we can calculate the mortgage reduction for the future value of an annuity due after 5 years:

FV = £2,000 * (((1 + 0.058/12)**(12*5) - 1) / (0.058/12)) * (1 + 0.058/12) &approx £138,385

Free Cash FLow from Paying off Mortgage

After paying off the mortgage early, the extra cash flow would be substantial.

2-Year Scenario

Monthly Cash Flow: £2000 * (1 + 0.058/12)**(12*2) / ((1 + 0.058/12)**(12*2) - 1) = £2,200

5-Year Scenario

Monthly Cash Flow: £2000 * (1 + 0.058/12)**(12*5) / ((1 + 0.058/12)**(12*5) - 1) = £2,500

Summary

Based on the assumptions and calculations above, it’s clear that investing in the stock market can yield higher returns compared to paying off the mortgage early. However, the decision ultimately depends on the risk tolerance, financial goals, and personal circumstances. It’s essential to consider the opportunity cost of investing in the stock market versus the guaranteed savings from paying off the mortgage early.

Investing in Stocks:

  • 2-Year Scenario Return: £51,362 - £52,894
  • 5-Year Scenario Return: £143,186 - £154,875

Paying off Mortgage:

  • 2-Year Scenario Savings: £51,617
  • 5-Year Scenario Savings: £138,385

Free Cash Flow from Paying off Mortgage:

  • 2-Year Scenario: £2,200
  • 5-Year Scenario: £2,500

Conclusion

  • For a 2-year horizon, investing in stocks might yield higher returns (7.0% to 10.19%) compared to the guaranteed savings from paying off the mortgage (7.53%), but comes with higher risk.
  • For a 5-year horizon, investing in stocks likely provides higher returns (19.32% to 29.06%) compared to paying off the mortgage (15.32%). However, the market risk remains.
  • Extra cash flow from paying off the mortgage early would significantly enhance your monthly savings once the mortgage is fully paid off.

This analysis provides a clear comparison to help you decide based on your risk tolerance and preference for guaranteed savings versus potential higher returns.

Interesting Notes

The analysis above was fully generated by GPT4o model. I tried to validate the numbers, it appears that there are some margin of errors in the calculations around £1,000 - £2,000 each time I asked the modle to generate the result of the formula. Anthropic Claude 3 also generated similar numbers but not the same as GPT4o.

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