Calculate the final loan amount of a 22500 auto loan with a 3.2% simple interest rate over a 5-year term.
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.
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.
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.
That is incorrect.
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.
The answers are
580.00
86.14
583.20
586.14
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.