For the investment compounded semi-annually, what information is necessary to determine the ratio of interest earned in the fourth year to the second year?

To determine the ratio of interest earned in the fourth year to the interest earned in the second year for an investment compounded semi-annually, both the principal amount and the interest rate are essential pieces of information.

The interest earned in any specific year can be calculated using the formula for compound interest. When interest is compounded semi-annually, the annual interest rate needs to be adjusted to reflect how it is compounded over two periods each year. The principal amount is critical to compute the actual interest earned in any given year since the amount of interest is directly proportional to the principal.

In the second year, the interest would be calculated based on the principal compounded for one full year (consisting of two compounding periods). For the fourth year, the interest calculation would involve the principal compounded over three full years (six compounding periods). The actual interest amounts can be determined once you have both the principal and the interest rate.

Thus, knowing both the principal amount and the interest rate allows you to accurately calculate and compare the interest earned in the specified years, leading to the determination of the desired ratio.