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Nathaniel invested $2,900 in an account paying an interest rate of 5.4% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 11 years?

Respuesta :

mhanifa

Answer:

  • $5252.53

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Given

  • Invested amount P = $2900,
  • Annual interest rate r = 5.4% = 0.054,
  • Time t = 11 years,
  • Compound number = continuous.

Find the balance after 11 years

Use equation for continuous compound:

  • [tex]P(t) = P_0e^{tr}[/tex],
  • where P(t) - final amount, Pā‚€ - initial amount, t - time, r - interest rate

Plug in the values and calculate:

  • [tex]P(11) = 2900e^{11*0.054}=5252.53 \ rounded[/tex]
semsee45

Answer:

$5,252.53 (nearest cent)

Step-by-step explanation:

Continuous Compounding Formula

[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]

where:

  • A = Final amount.
  • P = Principal amount.
  • e = Euler's number (constant).
  • r = Annual interest rate (in decimal form).
  • t = Time (in years).

Given values:

  • P = $2,900
  • r = 5.4% = 0.054
  • t = 11 years

Substitute the given values into the formula and solve for A:

[tex]\implies \sf A=2900 \cdot e^{(0.054 \cdot 11)}[/tex]

[tex]\implies \sf A=2900 \cdot e^{0.594}[/tex]

[tex]\implies \sf A=2900 \cdot 1.81121882[/tex]

[tex]\implies \sf A=5252.53457...[/tex]

Therefore, assuming no deposits or withdrawals are made, the amount of money in the account after 11 years would be $5,252.53 (nearest cent).

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