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How many years are needed for the loan to mature from 100000 to 250000 at thr quarterly interest rate of 7%

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Three and a half years are needed for the loan to mature from 100000 to 250000 at a quarterly interest rate of 7 %.

Let suppose that loan amount increases according to compound interest model, which is represented by:

[tex]C = C_{o}\cdot (1+r)^{t}[/tex] (1)

Where:

  • [tex]C_{o}[/tex] - Initial loan
  • [tex]C[/tex] - Current amount
  • [tex]r[/tex] - Interest rate
  • [tex]t[/tex] - Number of periods

If we know that [tex]C_{o} = 100000[/tex], [tex]C = 250000[/tex] and [tex]r = 0.07[/tex], then the needed number of periods is:

[tex]250000 = 100000\cdot (1+0.07)^{t}[/tex]

[tex]2.5 = (1+0.07)^{t}[/tex]

[tex]\log 2.5 = t\cdot \log 1.07[/tex]

[tex]t = \frac{\log 2.5}{\log 1.07}[/tex]

[tex]t \approx 13.543[/tex]

Given that 4 quarters are equal to a year, then we have that three and a half years are needed for the loan to mature from 100000 to 250000 at a quarterly interest rate of 7 %.

To learn more on compound interest, we kindly invite to check this question: https://brainly.com/question/7420113

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