Question

Brandi earned $78 in interest after one and one-half years on an account that paid 7.5% simple interest annually. Use the formula I = Prt to find Brandi's principal balance. Round to the nearest hundredth.

a) $87.75
b) $69.33
c) $693.33
d) $86.25

Answer 1

Brandi's principal balance was calculated by using the simple interest formula I = Prt, where I is the interest earned, P is the principal balance, r is the annual interest rate, and t is the time in years. Solving for P given I = $78, r = 7.5%, and t = 1.5 years, the principal balance comes out to $693.33.

Step-by-step explanation:

Brandi accumulated $78 in interest over a period of one and one-half years (1.5 years) using a simple interest rate of 7.5% annually. To calculate her principal balance using the formula I = Prt (Interest = Principal × rate × time), we first convert the percentage into a decimal by dividing by 100. Given the interest (I) is $78, the rate (r) is 0.075, and the time (t) is 1.5 years, the equation will look like:

$78 = P × 0.075 × 1.5

To find the principal (P), we divide both sides of the equation by (0.075 × 1.5):

P = $78 ÷ (0.075 × 1.5) = $78 ÷ 0.1125 = $693.33

Therefore, the principal balance that Brandi originally deposited into her account was $693.33, which makes the correct answer option (c).