The formula $\mathrm{A}=\mathrm{P}(1+\mathrm{r})^{2}$ gives the amount $\mathrm{A}$ in dollars that $\mathrm{P}$ dollars will grow to in 2 years at interest rate $r$ (where $r$ is given as a decimal), using compound interest. Use the formula $A=P(1+$ r) ${ }^{2}$ to find what the rate of interest is if a principal amount of $\$ 4000$ grows to $\$ 5017.60$ in 2 years, if interest is compounded annually.
A) $12 \%$
B) $13 \%$
C) $10 \%$
D) $14 \%$

Question

Quizplus · Accepted Answer

The formula is $5017.60 = 4000(1 + r)^2$. Solving for $r$, we get $1 + r = \sqrt{5017.60/4000}$. This gives $r \approx 0.12$, or 12%.

The Formula A=P(1+r)2\mathrm{A}=\mathrm{P}(1+\mathrm{r})^{2}A=P(1+r)2 Gives the Amount A\mathrm{A}A In Dollars That P\mathrm{P}P Dollars Will Grow to in 2 Years at Interest Rate

The Formula $\mathrm{A}=\mathrm{P}(1+\mathrm{r})^{2}$ Gives the Amount $\mathrm{A}$ In Dollars That $\mathrm{P}$ Dollars Will Grow to in 2 Years at Interest Rate