suppose henry places $4000 in an account that pays 13% interest compounded each year. assume that no…
suppose henry places $4000 in an account that pays 13% 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 $A = P(1 + r)^n$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $n$ is the number of years. Here, $P=$4000$, $r = 0.13$, and for part (a) $n = 1$. $A_1=4000\times(1 + 0.13)^1$
Step2: Calculate amount after 1 year
$A_1=4000\times1.13=$4520$
Step3: Calculate amount after 2 years
For part (b), $n = 2$. Using the compound - interest formula $A = P(1 + r)^n$ with $P = 4000$, $r=0.13$, and $n = 2$. $A_2=4000\times(1 + 0.13)^2=4000\times1.13^2=4000\times1.2769=$5107.6$
Answer:
(a) $$4520$ (b) $$5107.6$