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 $5500 grows to $6415.20 in two years, what is the interest rate?
A) 6%
B) 10%
C) 9%
D) 8%

Question

Quizplus · Accepted Answer

To find the interest rate, we can rearrange the formula to solve for $r$. Given $A = 6415.20$ and $P = 5500$, we substitute these values into the formula $A = P(1 + r)^2$ to get $6415.20 = 5500(1 + r)^2$. Dividing both sides by 5500 gives $1.1664 = (1 + r)^2$. Taking the square root of both sides gives $1.08 = 1 + r$, which means $r = 0.08$ or 8%.

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

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