carter invested $260 in an account paying an interest rate of 5.7% compounded annually. assuming no deposits…
carter invested $260 in an account paying an interest rate of 5.7% compounded annually. assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 6 years?
Answer
Explanation:
Step1: Identify compound - interest formula
The compound - interest formula is $A = P(1 + r)^t$, where $A$ is the amount of money in the account after $t$ years, $P$ is the principal amount (initial investment), $r$ is the annual interest rate (in decimal form), and $t$ is the number of years.
Step2: Convert the interest rate to decimal
The annual interest rate $r = 5.7%=0.057$. The principal amount $P=$260$ and the number of years $t = 6$.
Step3: Substitute values into the formula
$A=260\times(1 + 0.057)^6$. First, calculate $(1 + 0.057)^6$. $(1 + 0.057)^6=1.057^6\approx1.4071$. Then, $A = 260\times1.4071=365.846$.
Answer:
$$365.85$