Question

Holly is taking out a loan in the amount of $10,000. Her choices for the loan are a 6-year loan at a 4% annual simple interest and a 4-year loan at 3.75% annual compound interest. What is the difference in the amount of interest Holly would have to pay for each of these two loans?

Answer 1

To calculate the difference in the amount of interest Holly would have to pay for each loan, use the simple interest formula for the 6-year loan and the compound interest formula for the 4-year loan. The difference amounts to $796.87.

Step-by-step explanation:

To calculate the amount of interest Holly would have to pay for each loan, we need to use the formula:

Simple Interest = Principal * Rate * Time

Compound Interest = Principal * (1 + Rate/100)^(Time) - Principal

For the 6-year loan at 4% simple interest:

1. Principal = $10,000, Rate = 4%, Time = 6 years.
2. Simple Interest = $10,000 * 4% * 6 = $2,400

For the 4-year loan at 3.75% compound interest:

1. Principal = $10,000, Rate = 3.75%, Time = 4 years.
2. Compound Interest = $10,000 * (1 + 3.75/100)^(4) - $10,000 = $1,603.13

The difference in the amount of interest Holly would have to pay for each loan is $2,400 - $1,603.13 = $796.87.