Answer: We can use both formulas to calculate the interest on an investment of $3500 at 2.75% for 3 years.
Using the formula A = P(1+r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate as a decimal, n is the number of times interest is compounded per year, and t is the time in years, we have:
A = 3500(1+0.0275/1)^(1*3) ≈ $3843.84
Therefore, the interest earned is:
Interest = A - P = $3843.84 - $3500 = $343.84
Using the formula A = Pe^(rt), where A is the final amount, P is the principal amount, r is the annual interest rate as a decimal, t is the time in years, and e is the mathematical constant approximately equal to 2.71828, we have:
A = 3500e^(0.0275*3) ≈ $3843.84
Therefore, the interest earned is:
Interest = A - P = $3843.84 - $3500 = $343.84
The interest earned is $343.84 in both cases.