Question - Calculating Continuous Compounding Interest
Solution:
To solve this problem, we use the formula for continuous compounding interest:A = P * e^(rt)Where:A = the amount of money accumulated after n years, including interest.P = the principal amount (the initial amount of money)r = the annual interest rate (decimal)t = the time the money is invested for, in yearse = the mathematical constant approximately equal to 2.71828Given:P = $1,800r = 3.7% per annum = 0.037 (as a decimal)t = 10 yearsWe can now substitute the given values into the formula to find the value of the account after 10 years:A = 1800 * e^(0.037 * 10)Calculating the exponent first:0.037 * 10 = 0.37Now, raise e to the power of 0.37:e^0.37 is approximately 1.4481Now multiply this by the principal amount:A = 1800 * 1.4481 ≈ 2606.58Rounding to the nearest dollar, we get A ≈ $2,607.Therefore, the correct answer, rounded to the nearest dollar, is about $2,607 which corresponds to option C.
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