Final answer:
The effective annual rate (EAR) of a loan with a 12.50 percent APR that is compounded monthly is approximately 13.07%.
Step-by-step explanation:
The subject of the question involves calculating the effective annual rate (EAR) based on a given annual percentage rate (APR), which is a common concept in finance and mathematics. EAR takes into account the effects of compound interest which APR doesn't consider. Assuming that the APR mentioned is compounded monthly (which is typically the case for most loans), we can use the formula to convert APR to EAR:
EAR = (1 + (APR/n)) ^n - 1
With an APR of 12.50% compounded monthly, the calculation would be:
EAR = (1 + (0.1250/12)) ^(12) - 1
EAR = (1 + 0.0104167) ^12 - 1
EAR = (1.0104167) ^12 - 1
EAR ≈ 0.1307 or 13.07%
Therefore, the loan's effective annual rate is approximately 13.07%.