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 $\mathrm { A } = \mathrm { P } ( 1 + \mathrm { r } ) ^ { 2 }$ If a principal amount of $4500 grows to $5445.00 in two years, what is the interest rate?
A) 12%
B) 10%
C) 8%
D) 11%

Question

Quizplus · Accepted Answer

To find the interest rate, r, we can use the formula $A = P(1 + r)^2$ with $A = 5445$, $P = 4500$, and solve for $r$. Plugging in the values, we get $5445 = 4500(1 + r)^2$. Dividing both sides by 4500 gives $1.21 = (1 + r)^2$. Taking the square root of both sides gives $1.1 = 1 + r$, so $r = 0.1$ or 10%.

If an Amount of Money, Called the Principal, P, Is A=P(1+r)2\mathrm { A } = \mathrm { P } ( 1 + \mathrm { r } ) ^ { 2 }A=P(1+r)2

If an Amount of Money, Called the Principal, P, Is $\mathrm { A } = \mathrm { P } ( 1 + \mathrm { r } ) ^ { 2 }$