solve the problem. round to the nearest cent....

solve the problem. round to the nearest cent. barrys savings account has a balance of $2874. after 9 years, what will the amount of interest be at 5% compounded annually? a. $1589.52 c. $1575.52 b. $1584.52 d. $1437.00

Answer

# Explanation: ## Step1: Recall compound - interest formula The compound - interest formula is $A = P(1 + r)^t$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), $t$ is the number of years, and $A$ is the amount of money accumulated after $n$ years, including interest. Here, $P=\$2874$, $r = 0.05$, and $t = 9$. ## Step2: Calculate the amount $A$ $A=2874\times(1 + 0.05)^9$. First, calculate $(1 + 0.05)^9=1.05^9\approx1.551328$. Then, $A = 2874\times1.551328\approx4459.52$. ## Step3: Calculate the interest $I$ The interest $I=A - P$. Substitute $A\approx4459.52$ and $P = 2874$ into the formula. $I=4459.52-2874=\$1585.52$. # Answer: a. $\$1585.52$