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Steve invests $1,800 in an account that earns 3.7% annual interest, compounded continuously.
What is the value of the account after 10 years? Round your answer to the nearest dollar.

A. about $2,466
B. about $2,589
C. about $2,601
D. about $2,606

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Answer:

D. about $2,606

Step-by-step explanation:

Formula for Accrued Amount When Compounded Continuously

We can directly use the formula for accrued amount (final value of account) when interest is compounded continuously

This formula is
[tex]A = Pe^{rt}[/tex]

where
A is the final value
P is the amount invested (the principal)
r is the annual interest expressed as a decimal
t = time in years

Solution

We are given
P = 1800
Interest rate = 3.7%
t = 10 years

  • First convert interest rate to decimal:
    r = 3.7/100 = 0.037
  • Find rt which is the exponent in the equation
    rt = 0.037 x 10 = 0.37
  • Next, apply the formula with these values
    [tex]A = \$1800e^{0.37} \\A = \$2,605.92\\A = \$2606 \textrm{ rounded to the nearest \$}[/tex]
  • The above corresponds to choice D

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