Question

Jack borrows $5000 on loan that has an annual interest rate of 7.5%. He does not make any payments on the loan for the first 5 years. Which equation can be used to determine how much Jack will owe in total after 5 years?

1) A = P(1 + rt)
2) A = P(1 + r)ᵗ
3) A = P(1 - rt)
4) A = P(1 - r)ᵗ

Answer 1

The equation to determine how much Jack will owe after 5 years with simple interest is A = P(1 + rt), where A is the total amount, P is the principal, r is the annual interest rate, and t is the time in years.

Step-by-step explanation:

To determine how much Jack will owe in total after 5 years on a loan of $5000 with an annual interest rate of 7.5%, without making any payments, we need an equation that calculates the future value of a loan using simple interest. The correct formula for simple interest is Principal + (principal × rate × time). As per the options provided:

1. A = P(1 + rt) properly represents the simple interest formula, where A is the total amount owed, P is the principal amount, r is the annual interest rate in decimal form, and t is the time in years.
2. A = P(1 + r)ᵗ properly represents the compound interest formula, which is not applicable here.
3. A = P(1 - rt) suggests a decrease over time, which does not apply to interest growth.
4. A = P(1 - r)ᵗ also suggests a decrease over time and is incorrect.

Therefore, equation 1) A = P(1 + rt) is the equation that can be used to determine Jack's total debt after 5 years.