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 $100,000 or more. 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 12.25%
$20,000–$99,999 9.99%
>$99,999 6.75%
*interest rates are compounded quartely
First Bank of Lending Loan APR
Loan Amount APR*
<$20,000 12.25%
$20,000–$99,999 9.99%
>$99,999 6.75%
*interest rates are compounded quartely
Answers
GPT 3.5
To find the APY for a loan amount of $100,000 or more, we will use the formula for compound interest:
APY = (1 + (APR / n))^n - 1
Where APR is the annual percentage rate and n is the number of compounding periods per year (in this case, quarterly compounding means n=4).
For a loan amount greater than $99,999 with an APR of 6.75%, the calculation is as follows:
APY = (1 + (0.0675 / 4))^4 - 1
APY = (1 + 0.016875)^4 - 1
APY = (1.016875)^4 - 1
APY = 1.069892 - 1
APY = 0.069892
Therefore, the APY for a loan amount of $100,000 or more with an APR of 6.75% is 6.99%.
APY = (1 + (APR / n))^n - 1
Where APR is the annual percentage rate and n is the number of compounding periods per year (in this case, quarterly compounding means n=4).
For a loan amount greater than $99,999 with an APR of 6.75%, the calculation is as follows:
APY = (1 + (0.0675 / 4))^4 - 1
APY = (1 + 0.016875)^4 - 1
APY = (1.016875)^4 - 1
APY = 1.069892 - 1
APY = 0.069892
Therefore, the APY for a loan amount of $100,000 or more with an APR of 6.75% is 6.99%.