Compare simple interest at 3% and compound interest at 2% with interest being compounded monthly when $750 is invested for 1 year to determine which interest earning type offers more financial gains.
To compare simple interest at 3% and compound interest at 2% with interest being compounded monthly, we need to calculate the total amount earned in each scenario.
For simple interest at 3%, the formula to calculate the total amount is:
Total amount = principal * (1 + (interest rate * time))
In this case, the principal is $750, the interest rate is 3% (or 0.03), and the time is 1 year. Plugging these values into the formula:
Total amount = $750 * (1 + (0.03 * 1))
Total amount = $750 * (1 + 0.03)
Total amount = $750 * 1.03
Total amount = $772.50
Therefore, the total amount earned with simple interest at 3% is $772.50.
For compound interest at 2% compounded monthly, the formula to calculate the total amount is:
Total amount = principal * (1 + (interest rate / number of compounding periods))^(number of compounding periods * time)
In this case, the principal is $750, the interest rate is 2% (or 0.02), the number of compounding periods per year is 12 (since it is compounded monthly), and the time is 1 year. Plugging these values into the formula:
Total amount = $750 * (1 + (0.02 / 12))^(12 * 1)
Total amount = $750 * (1 + 0.0016667)^(12)
Total amount = $750 * (1.0016667)^(12)
Total amount = $750 * 1.02020134
Total amount ≈ $765.15
Therefore, the total amount earned with compound interest at 2% compounded monthly is approximately $765.15.
Comparing the two amounts, we can see that simple interest at 3% yields a total amount of $772.50, while compound interest at 2% compounded monthly yields a total amount of approximately $765.15. Hence, in this case, simple interest provides slightly more financial gains than compound interest.