Question

Suppose that a loan of $7500 is given at an interest rate of 7% compounded each year.
Assume that no payments are made on the loan.
Follow the instructions below. Do not do any rounding.
(a) Find the amount owed at the end of 1 year.
(b) Find the amount owed at the end of 2 years.

Answer 1

Answer:

(a) $8025

(b) $8586.75

General Formulas and Concepts:

Pre-Algebra

• Order of Operations: BPEMDAS

Algebra I

Compounded Interest Rate Formula: A = P(1 + r/n)ⁿˣ

• A is final amount
• P is principal (initial) amount
• r is rate
• n is compounded rate
• x is time (in years)

Step-by-step explanation:

Step 1: Define

P = 7500

r = 0.07

n = 1

Step 2: Write general formula

1. Substitute:          A = 7500(1 + 0.07/1)¹ˣ
2. Evaluate:            A = 7500(1.07)ˣ

Step 3: Solve

x = 1 year

1. Substitute:                    A = 7500(1.07)¹
2. Evaluate:                       A = 7500(1.07)
3. Multiply:                        A = 8025

x = 2 years

1. Substitute:                    A = 7500(1.07)²
2. Evaluate:                       A = 7500(1.1449)
3. Multiply:                        A = 8586.75

And we have our final answers!