Answer:
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,
- i represents the interest rate in annual terms
- n represents the number of compounding periods per year
- t is the time period in years
As the compounding is done semi annually, we can say that the interest is compounded 2 times in a year. Thus, n = 2
<u>At 5 % semi annual compounding</u>
Interest earned = 34000 * (1 + 0.05/2)^(7*2) - 34000
Interest earned = $14041.1099 rounded off to $14041.11
<u>At 6 % semi annual compounding</u>
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
