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Chemistry Asked by a SnapAndSolve user · about 20 hours ago

A loan is compounded semi-annually for 10 years. At the end of each compounding period, an interest rate of...

13. A loan is compounded semi-annually for 10 years. At the end of each compounding period, an interest rate of 2.75% is charged. Find the annual interest rate and the number of compounding periods.
The annual interest rate is 6.5%, and the number of compounding periods is 40.
The annual interest rate is 8.5%, and the number of compounding periods is 30.
The annual interest rate is 5.5%, and the number of compounding periods is 20.
The annual interest rate is 7.5%, and the number of compounding periods is 20.

Answer

Solution: Since the loan is compounded semi-annually for 10 years, the number of compounding periods is 2 times per year times 10 years, which equals 20 periods. The effective annual interest rate can be calculated using the formula for compound interest: (1 + r/n)^(n*t) - 1, where r is the nominal rate per period, n is the number of compounding periods per year, and t is the number of years.

Given that the interest rate per compounding period is 2.75%, the nominal annual interest rate is 2 * 2.75% = 5.5%. Therefore, the correct answer is:

  1. The annual interest rate is 5.5%, and the number of compounding periods is 20.

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