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If P dollars is deposited in a savings account that pays interest at a rate of r % per year compounded continuously, find the balance after t years. (Round your answer to the nearest cent.)
P = 800, r = 6 1/4, t = 4

Respuesta :

Answer:

Step-by-step explanation:

The formula for continuously compounded interest is

A = P x e (r x t)

Where

A represents the future value of the investment after t years.

P represents the present value or initial amount invested

r represents the interest rate

t represents the time in years for which the investment was made.

e is the mathematical constant approximated as 2.7183.

From the information given,

P = $800

r = 6.25% = 6.25/100 = 0.0625

t = 4 years

Therefore,

A = 800 x 2.7183^(0.0625 x 4)

A = 800 x 2.7183^(0.25)

A = $1288.0

Lanuel

The balance after t years (to the nearest cent) is equal to $1,019.52

Given the following data:

  • Principal = $800
  • Interest rate = [tex]6\frac{1}{4} = \frac{25}{4}[/tex] = 6.25%
  • Time = 4 years

To determine the balance after t years:

Mathematically, compound interest is given by the formula:

[tex]A = P(1 + r)^{t}[/tex]

Where;

  • A is the future value.
  • P is the principal or starting amount.
  • r is annual interest rate.
  • t is the number of years for the compound interest.

Substituting the given parameters into the formula, we have;

[tex]A = 800(1 + 0.0625)^{4}\\\\A = 800(1.0625)^{4}\\\\A =800 \times 1.2744[/tex]

A = $1,019.52

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