Question

Allison accumulated $7,000 in credit card debt. If the interest rate is 15% per year and she does not make any payments for 3 years, how much will she owe on this debt in 3 years for quarterly compounding? Round your answer to two decimal places.

Answer 1

Allison will owe $10,888.50 in 3 years

Explanation:

FV=PV(1+r/n)^nt

Where,

PV=$7000

r=15%=0.15

n=quarterly=4

t=3 years

FV=PV(1+r/n)^nt

=7000(1+0.15/4)^4*3

=7000(1+0.0375)^12

=7000(1.0375)^12

=7000(1.5555)

=10,888.50

To 2 decimal places=$10,888.50

Allison will owe $10,888.50 in 3 years

Answer 2

$10,888.20

Explanation:

Order of Operations: BPEMDAS

Compounded Interest Rate Formula: A = P(1 + r/a)ᵃᵇ

A = Final Amount

P = Initial Amount

r = rate

a = Compounded number

b = time

Step 1: Define

P = 7000

r = 15% = 0.15

a = 4

b = 3 years

Step 2: Solve for A

1. Substitute: A = 7000(1 + 0.15/4)⁴⁽³⁾
2. Parenthesis: A = 7000(1.0375)⁴⁽³⁾
3. Exponents: A = 7000(1.0375)¹²
4. Exponents: A = 7000(1.55545)
5. Multiplication: A = 10888.20

At the end of the 3 years that elapsed, Allison will have to pay a final debt of $10,888.20.