suppose that $6500 is placed in an account th...
suppose that $6500 is placed in an account that pays 18% interest compounded each year. assume that no withdrawals are made from the account. follow the instructions below. do not do any rounding. (a) find the amount in the account at the end of 1 year. $ (b) find the amount in the account at the end of 2 years. $
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), and $t$ is the number of years. Here, $P=\$6500$, $r = 0.18$, and for part (a), $t = 1$.
## Step2: Calculate amount after 1 year
Substitute the values into the formula: $A_1=6500\times(1 + 0.18)^1=6500\times1.18 = 7670$.
## Step3: Calculate amount after 2 years
For part (b), $t = 2$. Using the formula $A = P(1 + r)^t$, we substitute $P = 6500$, $r=0.18$, and $t = 2$. So $A_2=6500\times(1 + 0.18)^2=6500\times1.18^2=6500\times1.3924 = 9050.6$.
# Answer:
(a) $7670
(b) $9050.6