Answered

Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Experience the ease of finding accurate answers to your questions from a knowledgeable community of professionals. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

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

Sagot :

xero099

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

Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.