Final answer:
To calculate the effective annual interest rate (EAR) for a daily compounded APR of 5.95%, use the formula EAR = (1 + (APR/n))^n - 1. Once calculated, it will show a more accurate cost of the loan compared to simple interest calculations.
Step-by-step explanation:
The question at hand involves finding the effective annual interest rate (EAR) for a daily compounded interest rate of 5.95%. The EAR can be calculated using the formula:
EAR = (1 + (APR/n))^n - 1
Where APR is the annual percentage rate, and n is the number of times the interest is compounded per year.
In this case, since the APR is 5.95% and the compounding is daily (n = 365 days), the EAR would be calculated as follows:
EAR = (1 + (0.0595/365))^(365) - 1
Once calculated, this will give you the effective annual interest rate for the loan that Steven Garcia borrowed, providing a more accurate reflection of the true cost of borrowing when interest is compounded more frequently than annually.
The importance of understanding EAR comes to light in contrast to simple interest calculations. For instance, a $5,000 loan over three years with a simple interest rate of 6% would have a total interest of $900, calculated by multiplying the principal by the interest rate and the time period ($5,000 * 0.06 * 3).
However, with compound interest and daily compounding in particular, the amount of interest accrued can be significantly higher due to interest earned on accumulated interest. This illustrates why EAR can provide a clearer picture of the actual cost of a loan or investment.