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What is the maturity value of a loan of $11,315 from a bank on March 18 and repaid the loan on July 12 at 7% ordinary interest? Do not round off values in intermediate calculations.Round off  only the final answer to the nearest dollar. Do not include the currency sign in the answer.

Question

What is the maturity value of a loan of $11,315 from a bank on March 18 and repaid the loan on July 12 at 7% ordinary interest? Do not round off values in intermediate calculations.Round off  only the final answer to the nearest dollar. Do not include the currency sign in the answer.

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Solution

To calculate the maturity value of a loan, we first need to calculate the interest. The formula for ordinary interest (also known as simple interest) is:

Interest = Principal * Rate * Time

Where:

  • Principal is the initial amount of the loan, which is $11,315.
  • Rate is the annual interest rate, which is 7% or 0.07 in decimal form.
  • Time is the length of the loan in years.

The loan was taken out on March 18 and repaid on July 12. This is a period of about 3 months and 24 days. To convert this to a fraction of a year, we divide by 365 (the number of days in a year). So, the time is approximately (31 days in March - 18 days + 30 days in April + 31 days in May + 12 days in June) / 365 = 86/365 = 0.2356 years.

Now we can calculate the interest:

Interest = 11,3150.070.2356=11,315 * 0.07 * 0.2356 = 185.67

The maturity value of the loan is the sum of the principal and the interest. So:

Maturity Value = Principal + Interest = 11,315+11,315 + 185.67 = $11,500.67

Rounding to the nearest dollar, the maturity value of the loan is $11,501.

This problem has been solved

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