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a small business owner is applying for a small business loan and has been approved for a $50,000 loan with a 6.15% annual interest. the first loan is a simple interest rate, the second loan compounds interest quarterly, and the third loan compounds interest continuously. the small business owner plans to pay off the loan in three years and 7 months. Determine the total value of the loan with the quarterly compounded interest.

User Caryann
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Answer: The total value of the loan with quarterly compounded interest is $60,109.34.

Explanation:

To calculate the total value of the loan with quarterly compounded interest, we can use the formula for compound interest:

A = P * (1 + r/n)^(nt)

where:

A = final amount (loan + interest)

P = principal (the original amount of the loan)

r = annual interest rate as a decimal

n = number of times the interest is compounded in a year

t = time in years

For the loan with quarterly compounded interest, the number of times the interest is compounded in a year is 4 (since interest is compounded quarterly), and the time is 3 years and 7 months, which we can convert to years as 3.5833.

Substituting the values into the formula, we get:

A = $50,000 * (1 + 0.0615/4)^(4 * 3.5833)

A = $50,000 * (1.015375)^(15.7532)

A = $50,000 * 1.22186888

A = $60,109.34

Therefore, To calculate the total value of the loan with quarterly compounded interest, we can use the formula for compound interest:

A = P * (1 + r/n)^(nt)

where:

A = final amount (loan + interest)

P = principal (the original amount of the loan)

r = annual interest rate as a decimal

n = number of times the interest is compounded in a year

t = time in years

For the loan with quarterly compounded interest, the number of times the interest is compounded in a year is 4 (since interest is compounded quarterly), and the time is 3 years and 7 months, which we can convert to years as 3.5833.

Substituting the values into the formula, we get:

A = $50,000 * (1 + 0.0615/4)^(4 * 3.5833)

A = $50,000 * (1.015375)^(15.7532)

A = $50,000 * 1.22186888

A = $60,109.34

Therefore, the total value of the loan with the quarterly compounded interest would be $60,109.34.

User Ophir Yoktan
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