Solve the problem.
-If an amount of money, called the principal, P, is deposited into an account that earns interest at a rate r, compounded annually, then in two years that investment will grow to an amount A, given by the formula
A = P(1 + r)2. If a principal amount of $4000 grows to $5198.40 in two years, what is the interest rate?
A) 14%
B) 16%
C) 12%
D) 15%

Question

Quizplus · Accepted Answer

The interest rate is 14%.The formula for the amount of money in an account after two years is A = P(1 + r)2. We know that the principal amount is $4000 and the amount after two years is $5198.40. So we can plug these values into the formula and solve for r:5198.40 = 4000(1 + r)25198.40 = 4000(1 + r)(1 + r)5198.40 = 4000(1 + 2r + r2)5198.40 = 4000 + 8000r + 4000r24000r2 + 8000r - 1198.40 = 0(200r - 14)(20r + 85.28) = 0r = 14 or r = -0.4264Since the interest rate cannot be negative, the only valid solution is r = 14%.

Solve the Problem. -If an Amount of Money, Called the Principal, P, Is