claire deposited $2,500 into an account that accrues interest monthly. she made no additional deposits or…

claire deposited $2,500 into an account that accrues interest monthly. she made no additional deposits or withdrawals. after 2 years, claire had $2,762.35 in the account. what is the annual interest rate of the account? compound interest formula: v(t)=p(1 + r/n)^nt t = years since initial deposit n = number of times compounded per year r = annual interest rate (as a decimal) p = initial (principal) investment v(t) = value of investment after t years 5% 11% 26% 31%

claire deposited $2,500 into an account that accrues interest monthly. she made no additional deposits or withdrawals. after 2 years, claire had $2,762.35 in the account. what is the annual interest rate of the account? compound interest formula: v(t)=p(1 + r/n)^nt t = years since initial deposit n = number of times compounded per year r = annual interest rate (as a decimal) p = initial (principal) investment v(t) = value of investment after t years 5% 11% 26% 31%

Answer

Explanation:

Step1: Identify the values

$P = 2500$, $V(t)=2762.35$, $n = 12$ (month - compounded), $t = 2$

Step2: Substitute into compound - interest formula

$2762.35=2500\left(1 +\frac{r}{12}\right)^{12\times2}$

Step3: Divide both sides by 2500

$\frac{2762.35}{2500}=\left(1 +\frac{r}{12}\right)^{24}$ $1.10494=\left(1 +\frac{r}{12}\right)^{24}$

Step4: Take the 24th root of both sides

$1.10494^{\frac{1}{24}}=1+\frac{r}{12}$ $1.004167 = 1+\frac{r}{12}$

Step5: Solve for $r$

$1.004167-1=\frac{r}{12}$ $0.004167=\frac{r}{12}$ $r=0.004167\times12$ $r = 0.05$ or $5%$

Answer:

A. 5%