Calculating Continuous Compounding Interest
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 years
e = the mathematical constant approximately equal to 2.71828
Given:
P = $1,800
r = 3.7% per annum = 0.037 (as a decimal)
t = 10 years
We 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 = 0.37
Now, raise e to the power of 0.37:
e^0.37 is approximately 1.4481
Now multiply this by the principal amount:
A = 1800 * 1.4481 ≈ 2606.58
Rounding 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.
