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lubasha [3.4K]
1 year ago
9

Consider an investment of $6000 that earns 4.5% interest.

Mathematics
1 answer:
miss Akunina [59]1 year ago
3 0

Answer:

20.4 years (nearest tenth)

Step-by-step explanation:

<u>Compound Interest Formula</u>

\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}

where:

  • A = final amount
  • P = principal amount
  • r = interest rate (in decimal form)
  • n = number of times interest applied per time period
  • t = number of time periods elapsed

Given:

  • A = $15,000
  • P = $6,000
  • r = 4.5% = 0.045
  • n = 12 (monthly)

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

\implies \sf 15000=6000\left(1+\frac{0.045}{12}\right)^{12t}

\implies \sf \dfrac{15000}{6000}=\left(1.00375\right)^{12t}

\implies \sf 2.5=\left(1.00375\right)^{12t}

\implies \sf \ln (2.5)=\ln \left(1.00375\right)^{12t}

\implies \sf \ln (2.5)=12t \ln \left(1.00375\right)

\implies \sf t=\dfrac{\ln (2.5)}{12 \ln (1.00375)}

\implies \sf t=20.40017123

Therefore, it would take 20.4 years (nearest tenth) for the investment to reach $15,000.

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