Final answer:
To determine which option is better based on the effective interest rate, we calculate the effective interest rate for both the simple interest note and the simple discount note. The effective interest rate for the simple discount note is 7.816%, making it the better option.
Step-by-step explanation:
To determine which option is better based on the effective interest rate, we need to calculate the effective interest rate for both the simple interest note and the simple discount note. The effective interest rate takes into account the time value of money and is used to compare different interest rates and terms.
For the simple interest note:
Interest = Principal * Rate * Time
= $33,353 * 0.07 * (18/12) = $33,353 * 0.105 = $3,501.465
Total amount to be paid back = Principal + Interest = $33,353 + $3,501.465 = $36,854.465
The effective interest rate for the simple interest note is:
Effective Interest Rate = (Total amount to be paid back / Principal - 1) * 100%
= ($36,854.465 / $33,353 - 1) * 100%
= (1.1077 - 1) * 100%
= 0.1077 * 100%
= 10.77%
For the simple discount note:
Discount = Principal * Rate * Time
= $33,353 * 0.07 * (18/12) = $33,353 * 0.105 = $3,501.465
Amount to be paid upfront = Principal − Discount = $33,353 − $3,501.465 = $29,851.535
The effective interest rate for the simple discount note is:
Effective Interest Rate = (Discount / Amount to be paid upfront) * (1 / Time) * 100%
= ($3,501.465 / $29,851.535) * (1 / (18/12)) * 100%
= 0.11725 * 0.6667 * 100%
= 0.07816 * 100%
= 7.816%
Based on the effective interest rates, the simple discount note with an effective interest rate of 7.816% would be the better option.