Question

Calculate the final loan amount of a 22500 auto loan with a 3.2% simple interest rate over a 5-year term.
Answer
Correct,
Next: Calculate the final loan amount of a $500 credit card loan with a 16% compound interest rate, compounded monthly, for a 1-year term.
Answer
That is incorrect.
Answer
The answers are
580.00
86.14
583.20
586.14
Answered by GPT 3.5
To calculate the final loan amount, we need to consider the formula for calculating simple interest:

Interest = Principal * Rate * Time

Where:
Principal = $22,500
Rate = 3.2% (converted to decimal form, 0.032)
Time = 5 years

Using this formula, we can calculate the interest:

Interest = $22,500 * 0.032 * 5 = $3,600

The total loan amount is the sum of the principal and the interest:

Final loan amount = Principal + Interest = $22,500 + $3,600 = $26,100

Therefore, the final loan amount for a $22,500 auto loan with a 3.2% simple interest rate over a 5-year term is $26,100.
Answered by GPT 3.5
To calculate the final loan amount with compound interest, we can use the formula:

Final loan amount = Principal * (1 + Rate/ n)^(n * Time)

Where:
Principal = $500
Rate = 16% (converted to decimal form, 0.16)
n = number of times interest is compounded per year (monthly, so n = 12)
Time = 1 year

Using these values, we can calculate the final loan amount:

Final loan amount = $500 * (1 + 0.16 / 12)^(12 * 1)

Now let's calculate the exponent part of the formula first:

Exponent = 12 * 1 = 12

Now, let's calculate the part inside the parentheses:

1 + (0.16 / 12) = 1 + 0.013333 = 1.013333

Now we raise this value to the power of 12:

1.013333^12 = 1.19561835808

Finally, multiply this value by the principal:

Final loan amount = $500 * 1.19561835808 = $597.81 (rounded to two decimal places)

Therefore, the final loan amount for a $500 credit card loan with a 16% compound interest rate, compounded monthly, for a 1-year term is approximately $597.81.
Answered by GPT 3.5
Apologies for the mistake. Let's recalculate the final loan amount correctly using compound interest.

The formula for compound interest is:

Final loan amount = Principal * (1 + Rate/ n)^(n * Time)

Where:
Principal = $500
Rate = 16% (converted to decimal form, 0.16)
n = number of times interest is compounded per year (monthly, so n = 12)
Time = 1 year

Using these values, we can calculate the final loan amount:

Final loan amount = $500 * (1 + 0.16 / 12)^(12 * 1)

1 + (0.16 / 12) = 1 + 0.013333 = 1.013333

Now we raise this value to the power of 12:

1.013333^12 ≈ 1.169859

Final loan amount = $500 * 1.169859 ≈ $584.93

Therefore, the final loan amount for a $500 credit card loan with a 16% compound interest rate, compounded monthly, for a 1-year term is approximately $584.93.
Answered by GPT 3.5
I apologize for the confusion. Let's recalculate the final loan amount correctly.

The formula for compound interest is:

Final loan amount = Principal * (1 + Rate/ n)^(n * Time)

Where:
Principal = $500
Rate = 16% (converted to decimal form, 0.16)
n = number of times interest is compounded per year (monthly, so n = 12)
Time = 1 year

Using these values, we can calculate the final loan amount:

Final loan amount = $500 * (1 + 0.16 / 12)^(12 * 1)

1 + (0.16 / 12) = 1 + 0.013333 = 1.013333

Now we raise this value to the power of 12:

1.013333^12 ≈ 1.19561835808

Final loan amount = $500 * 1.19561835808 ≈ $597.81

Apologies for the confusion again. The correct answer is $597.81.