Today, Jonathan is investing $34,000 at 5 percent, compounded semi-annually, for 7 years. How much additional income could Jonathan earn if he had invested this amount at 6 percent, compounded semi-annually

Additional Earnings = $3386.940745 rounded off to $3386.94

Explanation:

To calculate the amount of additional income, we must first calculate the interest earned at 5% and 6% semi annual compounding for 7 years and then deduct the interest earned at 6% from the interest earned at 5%. The formula to calculate the interest earned under semi annual compounding is,

Interest earned = Principal * (1 + i/n)^(t*n) - Principal

Where,

As the compounding is done semi annually, we can say that the interest is compounded 2 times in a year. Thus, n = 2

At 5 % semi annual compounding

Interest earned = 34000 * (1 + 0.05/2)^(7*2)  -  34000

Interest earned = $14041.1099 rounded off to $14041.11

At 6 % semi annual compounding

Interest earned = 34000 * (1 + 0.06/2)^(7*2)  -  34000

Interest earned = $17428.05065 rounded off to $17428.05

Additional earnings = 17428.05065  -   14041.1099

Additional Earnings = $3386.940745 rounded off to $3386.94