Question

To pay for a home improvement project that totals $20,000, a homeowner is choosing between two different credit card loans with an interest rate of 6%. the first credit card compounds interest semi-annually, while the second credit card compounds quarterly. the homeowner plans to pay off the loan in 10 years. determine the total value of the loan with the semi-annually compounded interest. show all work and round your answer to the nearest hundredth.

Answer 1

The total value of the loan with semi-annually compounded interest is approximately $36,122.20.

Step-by-step explanation:

To determine the total value of the loan with semi-annually compounded interest, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the total value of the loan, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years. In this case, the principal amount is $20,000, the annual interest rate is 6%, the interest is compounded semi-annually (n = 2), and the loan is for 10 years (t = 10).

Plugging in the values into the formula:

A = 20000(1 + 0.06/2)^(2*10)

A ≈ 20000(1.03)^(20)

A ≈ 20000 * 1.80611

A ≈ 36122.20

The total value of the loan with semi-annually compounded interest is approximately $36,122.20.

Answer 2

To calculate the total value of a loan with semi-annual compounding interest, the formula A = P(1 + r/n)^(nt) is used. For a loan of $20,000 with a 6% interest rate compounded semi-annually over 10 years, the total amount paid would be approximately $36,122.20.

Step-by-step explanation:

To determine the total value of a loan with semi-annual compounding interest, we can use the formula for the future value of a compound interest loan, which is A = P(1 + r/n)nt, where:

• P = principal amount (the initial amount of money)
• r = annual interest rate (decimal)
• n = number of times the interest is compounded per year
• t = time the money is invested or borrowed for, in years
• A = amount of money accumulated after n years, including interest.

In this scenario, P = $20,000, r = 6% or 0.06, n = 2 (as the interest is compounded semi-annually), and t = 10 years.

Using the formula:

A = 20000(1 + 0.06/2)2*10

A = 20000(1 + 0.03)20

A = 20000(1.03)20

A = 20000 * 1.80611...

The homeowner will have to pay approximately $36,122.20 to pay off the loan with semi-annual compounding interest after 10 years, rounding to the nearest hundredth.