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WILL GIVE BRAINLIEST Chang deposited $5000 into an account with a 4.8% annual interest rate, compounded monthly. Assuming that no withdrawals are made, how long will it take for the investment to grow to $7850 ?
Do not round any intermediate computations, and round your answer to the nearest hundredth.

Respuesta :

semsee45

Answer:

9.42 years (= 113 months)

Step-by-step explanation:

Use the compound rate interest formula:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

where:

  • A = amount
  • P = principal
  • r = interest rate (in decimal format)
  • n = number of times interest is compounded per unit t
  • t = time

Given:

  • A = $7850
  • P = $5000
  • r = 4.8% = 0.048
  • n = 12
  • t = years

[tex]\implies 7850=5000(1+\frac{0.048}{12})^{12t}[/tex]

[tex]\implies 7850=5000(1.004)^{12t}[/tex]

[tex]\implies \dfrac{7850}{5000}=(1.004)^{12t}[/tex]

[tex]\implies 1.57=(1.004)^{12t}[/tex]

Take natural logs:

[tex]\implies \ln1.57=\ln(1.004)^{12t}[/tex]

[tex]\implies \ln1.57=12t\ln(1.004)[/tex]

[tex]\implies t=\dfrac{\ln 1.57}{12 \ln1.004}[/tex]

[tex]\implies t=9.42\textsf{ years (nearest hundredth)}[/tex]

[tex]\implies t=113 \textsf{ months}[/tex]

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