Question

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:mc006-1.jpg

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 1

The annual interest rate is 5.247%. Subtract $2,500.00 from $2,762.35 and you get 262.35- the 2-year interest. To get the annual interest, divide 262.35 by 2, which equals 131.75. Then, divide 131.75 by 2,500 (original amount) and you get 0.05247. Lastly, multiply 0.05247 by 100 to get the answer (5.247%).

Answer 2

Answer:

A. 5%.

Step-by-step explanation:

We have been given that Claire deposited $2,500 into an account that accrues interest monthly. After 2 years, Claire had $2,762.35 in the account.

To find the interest rate we will use compound interest formula.

$A=P(1+\frac{r}{n})^{nt}$, where,

A = Value of investment after t years,

P = Principal amount,

r = Annual interest rate in decimal form,

n = Number of times interest in compounded per year,

t = Time in years.

Upon substituting our given values in compound interest formula we will get,  

$2762.35=2500(1+\frac{r}{12})^{12*2}$

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

Upon dividing both sides of our equation by 2500 we will get,

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

$1.10494=(1+\frac{r}{12})^{24}$      

Upon taking 24th root of both sides of our equation we will get,

$\sqrt[24]{1.10494}=\sqrt[24]{(1+\frac{r}{12})^{24}}$    

$1.0041666160936978=1+\frac{r}{12}$    

Let us subtract 1 from both sides of our equation.

$1.0041666160936978-1=1-1+\frac{r}{12}$

$0.0041666160936978=\frac{r}{12}$

Multiplying both sides of our equation by 12 we will get,

$0.0041666160936978\times 12=\frac{r}{12}\times 12$

$0.0499993931=r$

Since our rate is in decimal form, so we will multiply it by 100 to get rate as a percent.

$r=0.0499993931\times 100$

$r=4.99993931\approx 5$

Therefore, the annual interest rate of the account is 5% and option A is the correct choice.