suppose that $4000 is placed in an account that pays 9% interest compounded each year. assume that no…
suppose that $4000 is placed in an account that pays 9% 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 for 1 - year
The formula for compound interest when compounded annually is $A = P(1 + r)$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form). Given $P=$4000$ and $r = 0.09$. $A_1=4000\times(1 + 0.09)$
Step2: Calculate the amount after 1 year
$A_1=4000\times1.09 = 4360$
Step3: Recall compound - interest formula for 2 - years
The formula for compound interest when compounded annually for $n$ years is $A = P(1 + r)^n$. For $n = 2$, $P = 4000$, and $r=0.09$, we have $A_2=4000\times(1 + 0.09)^2$. $A_2=4000\times1.09^2$
Step4: Calculate the amount after 2 years
$A_2=4000\times1.1881=4752.4$
Answer:
(a) $4360 (b) $4752.4