Question

Wilson Montgomery was curious about the difference between a simple discount note and a simple interest note. He is considering taking out one or the other. Let him know which one he should take out based on proceeds and effective rate. Both have the same terms: $5,500 at 6% for 18 months. Round to the nearest tenth.

What is the answer to this question?

Answer 1

For the given terms, a simple discount note would provide higher loan proceeds and a slightly lower effective rate. Therefore, Wilson Montgomery should take out a simple discount note.

Step-by-step explanation:

A simple discount note and a simple interest note are two different types of loans. In a simple discount note, the interest is deducted upfront from the face value of the loan, and the borrower receives the remainder as the loan proceeds.

In a simple interest note, the interest is calculated and paid periodically over the duration of the loan, and the borrower receives the full face value as the loan proceeds.

For the given terms of $5,500 at 6% for 18 months, let's calculate the proceeds and effective rate for each type of loan.

Simple Discount Note:

1. Calculate the interest deducted upfront: Interest = Principal × Rate × Time = $5,500 × 6% × 1.5 years = $495
2. Calculate the loan proceeds: Loan Proceeds = Principal - Interest = $5,500 - $495 = $5,005
3. Calculate the effective rate: Effective Rate = (Interest / Loan Proceeds) × 100 = ($495 / $5,005) × 100 ≈ 9.9%

Simple Interest Note:

Calculate the interest paid periodically: Interest = Principal × Rate × Time = $5,500 × 6% × 1.5 years = $495

1. Calculate the loan proceeds: Loan Proceeds = Principal = $5,500
2. Calculate the effective rate: Effective Rate = (Interest / Loan Proceeds) × 100 = ($495 / $5,500) × 100 ≈ 9%

Based on the higher loan proceeds and slightly lower effective rate, Wilson Montgomery should take out a simple discount note.