contestada

A loan of $17,000 is made at 4% interest, compounded annually. After how many years will the amount due reach $23,000 or more? (Use the calculator
provided if necessary.)
Write the smallest possible whole number answer.
years
X
5

Respuesta :

semsee45

Answer:

8 years

Step-by-step explanation:

Annual Compound Interest Formula

[tex]\large \text{$ \sf A=P\left(1+r\right)^{t} $}[/tex]

where:

  • A = final amount
  • P = principal amount
  • r = interest rate (in decimal form)
  • t = time (in years)

Given values:

  • A = $23,000
  • P = $17,000
  • r = 4% = 0.04

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

[tex]\implies \sf 23000=17000(1+0.04)^t[/tex]

[tex]\implies \sf \dfrac{23000}{17000}=1.04^t[/tex]

[tex]\implies \sf \dfrac{23}{17}=1.04^t[/tex]

Take natural logs of both sides:

[tex]\implies \sf \ln \left(\dfrac{23}{17}\right) = \ln 1.04^t[/tex]

[tex]\textsf{Apply the power law}: \quad \ln x^n=n \ln x[/tex]

[tex]\implies \sf \ln \left(\dfrac{23}{17}\right) = t \ln 1.04[/tex]

[tex]\implies \sf t=\dfrac{\ln \left(\dfrac{23}{17}\right)}{\ln 1.04}[/tex]

[tex]\implies \sf t = 7.707174285...[/tex]

Therefore, the amount will reach $23,000 after 8 years.

Learn more about compound interest here:

https://brainly.com/question/27747709

https://brainly.com/question/28225117

Otras preguntas