Question
The First Bank of Lending lists the following APR for loans. Determine the APY, or effective interest rate, for a loan amount that is less than $20,000. Express your answer as a percentage rounded to the nearest hundredth of a percent, if necessary.
First Bank of Lending Loan APR
Loan Amount APR*
<$20,000 9.25%
$20,000–$99,999 6.99%
>$99,999 3.75%
*interest rates are compounded monthly
First Bank of Lending Loan APR
Loan Amount APR*
<$20,000 9.25%
$20,000–$99,999 6.99%
>$99,999 3.75%
*interest rates are compounded monthly
Answers
GPT 3.5
To calculate the APY for a loan amount that is less than $20,000 with an APR of 9.25% compounded monthly, we can use the formula:
APY = (1 + (APR/n))^n - 1
Where:
APR = Annual Percentage Rate
n = number of compounding periods per year
In this case, the APR is 9.25% and it is compounded monthly, so n = 12.
Plugging in the values, we get:
APY = (1 + (0.0925/12))^12 - 1
APY = (1 + 0.00770833333)^12 -1
APY = (1.00770833333)^12 -1
APY = 1.09380615779 -1
APY = 0.09380615779
Therefore, the APY for a loan amount less than $20,000 with an APR of 9.25% is approximately 9.38%.
APY = (1 + (APR/n))^n - 1
Where:
APR = Annual Percentage Rate
n = number of compounding periods per year
In this case, the APR is 9.25% and it is compounded monthly, so n = 12.
Plugging in the values, we get:
APY = (1 + (0.0925/12))^12 - 1
APY = (1 + 0.00770833333)^12 -1
APY = (1.00770833333)^12 -1
APY = 1.09380615779 -1
APY = 0.09380615779
Therefore, the APY for a loan amount less than $20,000 with an APR of 9.25% is approximately 9.38%.