To calculate the interest earnings for each option, we can use the following formulas:
Option 1 (Simple Interest):
Interest = Principal * Rate * Time
Option 2 (Compound Interest):
Final Amount = Principal * (1 + (Rate / n))^(n * Time)
Interest = Final Amount - Principal
Option 1:
Principal = $7,000
Rate = 15% = 0.15
Time = 3 years
Interest1 = $7,000 * 0.15 * 3
Interest1 = $3,150
Option 2:
Principal = $7,000
Rate = 12% = 0.12
n = 4 (quarterly compounding)
Time = 3 years
Final Amount2 = $7,000 * (1 + (0.12/4))^(4 * 3)
Final Amount2 ≈ $7,000 * (1.03)^(12)
Final Amount2 ≈ $7,000 * 1.425984
Final Amount2 ≈ $9,981.89
Interest2 = $9,981.89 - $7,000
Interest2 ≈ $2,981.89
To find the difference in interest earnings, we subtract the interest earned with option 1 from the interest earned with option 2:
Difference = Interest2 - Interest1
Difference ≈ $2,981.89 - $3,150
Difference ≈ -$168.11
The difference in interest earnings is approximately -$168.11. This means that option 2, investing with a 12% compound interest rate compounded quarterly, would generate less interest earnings compared to option 1, investing with a 15% simple interest rate.
Therefore, option 1 is the better investing option as it would give more financial returns.