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Write a function that represents the balance after t years.

$2000 deposit that earns 5% annual interest compounded quarterly

y =

Respuesta :

Answer:

[tex]Y=2,000[1.0125]^{4t}[/tex]

Step-by-step explanation:

Given:

Amount deposit P = $2,000

Time t = t year (yearly) = 4t(quarterly)

Rate r = 5% annual = 5/4 = 1.25% (quarterly) = 0.0125

Find:

Amount after t year (Y)

Computation:

A = P[1+r]ⁿ

So,

[tex]Y = 2,000[1+0.0125]^{4t} \\\\Y = 2,000[1.0125]^{4t}[/tex]

abidemiokin

A  function that represents the balance after t years is y = 2000(1.0125)^4t

Compound interest

The compound interest formula is expressed as:

A = P(1+r/n)^nt

Given

  • P = 2000
  • r = 0.05
  • t = t
  • n = 4

Substitute into the formula:

A(t) = 2000(1+0.05/4)^4t

y = 2000(1.0125)^4t

Hence a  function that represents the balance after t years is y = 2000(1.0125)^4t

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