Answered

Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Get quick and reliable solutions to your questions from a community of experienced professionals on our platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A 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

Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.