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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:
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