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 year

Answer 1

Answer:

r= 5%

Step-by-step explanation:

The formula for compounded interest is:

$A=P(1+\frac{I}{n})^{nt}$

Where 'A' is the amount of investment after t years, 'P' is the principal amount, 'r' is the interest rate, 'n' is the number of times interest is compounded per year, and t is the number of years.

Hence,

$2762.53=2500(1+\frac{r}{12})^{12*2}\\ \\1.105012=(1+\frac{r}{12})^{24}$

Take the 24th root:

$1.004169=1+\frac{r}{12}\\0.004169=\frac{r}{12}\\r=0.04992\\r=4.992\approx 5\%$

Answer 2

Answer:

A. R = 5%

Step-by-step explanation: