Solve the problem.
-If an amount of money, called the principal, $\mathrm { P }$, 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 $\$ 7147.80$ in two years, what is the interest rate?
A) $16 \%$
B) $14 \%$
C) $12 \%$
D) $15 \%$

Question

Quizplus · Accepted Answer

To find the interest rate, we use the formula $A = P(1 + r)^2$ with $A = 7147.80$ and $P = 5500$. Rearranging the formula to solve for $r$, we get $r = \sqrt{\frac{A}{P}} - 1$. Substituting the given values, we find $r = \sqrt{\frac{7147.80}{5500}} - 1$, which simplifies to $r = \sqrt{1.2996} - 1$. This gives $r \approx 0.14$ or $14\%$.

Solve the Problem P\mathrm { P }P , Is Deposited into an Account That Earns Interest at Principal

Solve the Problem $\mathrm { P }$ , Is Deposited into an Account That Earns Interest at Principal