Surprising Bank Investment

Your bank has proposed an investment opportunity in a new startup. If successful, you will get to keep all the profits after one year. They sweetened the deal by contributing a smaller portion, which they’ll take back after a year, but any profit on their share is yours. Excited about this, you’ve decided to invest a substantial amount: $1,000,000 in total, with 99% from you and 1% from the bank. However, a year later, you receive a letter saying the startup went bankrupt, resulting in some losses. The bank reassures you that you still own 98% of the remaining money, and they’ll take back their initial investment, leaving you with the rest. Should you be worried?

Let’s delve into the numbers. At first glance, it might not seem like a significant loss since the bank’s investment was only 1%. However, upon closer examination, the bank’s initial investment was $10,000 (1% of $1,000,000). Per the agreement, they’ll get this back regardless of the startup’s failure. With you owning 98% of the remaining funds, the other 2% ($10,000) belongs to the bank. So, if 2% equals $10,000, 98% corresponds to $490,000. In equation form, if \(x\) represents the remaining money after the investment, we can express it as:

\[\begin{align*} x &= $10\,000 + 0.98x \\ 0.02x &= $10\,000 \\ x &= \frac{$10\,000}{0.02} = 500\,000 $ \\ 0.98x &= 0.98 \cdot $500\,000 = $490\,000 \end{align*}\]

Considering you invested 99% of $1,000,000, which equals $990,000, you’ve actually lost $500,000. That’s over 50% of your original investment. So, it’s understandable if you’re not exactly amused by the outcome.