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Answer :
The amount in the account after seven years, with continuous compounding at a 2.5% rate, is closest to $4408.51. So correct option is not listed here.
The question asks to calculate the future value of an investment with continuous compounding.
To find the amount in the account after seven years, we use the formula for continuous compounding, which is A = Pert, where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), t is the time in years, and e is the base of the natural logarithm, approximately equal to 2.71828.
To apply this formula to the given scenario where P = $3700, r = 2.5% (or 0.025 as a decimal), and t = 7 years, we get: A = 3700 * e(0.025*7)
Now we will calculate the value:
- A = 3700 * 2.71828(0.025*7)
- A = 3700 * 2.71828(0.175)
- A ≈ 3700 * 1.19122
- A ≈ 4408.514
Therefore, the amount in the account after seven years will be approximately $4408.51. So correct option is not listed here.
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