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Jonah Breakspear purchased 100 shares of Berkshire Hathaway for $800 per share on January 1st, 1983. The shares were trading at a price of $480,000 on January 1st, 2023. Calculate the rate of return, compounded semi-annually, that Jonah realized on this investment

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Final answer:

To calculate the rate of return that Jonah realized on this investment, we can use the compound interest formula. By plugging in the provided values and solving for the annual interest rate (r), we find that Jonah realized a rate of return of 1.25% per year, compounded semi-annually, on this investment.

Step-by-step explanation:

To calculate the rate of return that Jonah realized on this investment, we can use the compound interest formula. The formula for compound interest is:

A = P(1 + r/n)^(nt)

Where:

  • A is the future value of the investment
  • P is the initial investment
  • r is the annual interest rate (in decimal form)
  • n is the number of times the interest is compounded per year
  • t is the number of years

In this case, the future value (A) is $480,000, the initial investment (P) is $800, the number of times the interest is compounded per year (n) is 2 (semi-annually), and the number of years (t) is 40 (from 1983 to 2023).

By plugging these values into the formula, we can solve for the annual interest rate (r). The formula becomes:

$480,000 = $800(1 + r/2)^(2*40)

Simplifying the equation, we get:

$600 = (1 + r/2)^80

Taking the 80th root of both sides, we get:

1.00625 = 1 + r/2

Solving for r, we get:

r/2 = 0.00625

r = 0.0125

Therefore, Jonah realized a rate of return of 1.25% per year, compounded semi-annually, on this investment.

User Priyansh Gupta
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