lakisha just won some money in a sweepstakes ...
lakisha just won some money in a sweepstakes drawing. she is considering putting her winnings in a long - term investment. to the nearest dollar, how much money would lakisha need to put into an account earning 5% interest compounded annually in order to have $30,000 at the end of 20 years?
Answer
# Explanation:
## Step1: Identify compound - interest formula
The compound - interest formula is $A = P(1 + r)^t$, where $A$ is the final amount, $P$ is the principal amount (initial investment), $r$ is the annual interest rate (as a decimal), and $t$ is the number of years. We want to find $P$, so we can rewrite the formula as $P=\frac{A}{(1 + r)^t}$.
## Step2: Convert values to correct form
We know that $A = 30000$, $r=0.05$ (since $5\%=0.05$), and $t = 20$.
## Step3: Substitute values into formula
$P=\frac{30000}{(1 + 0.05)^{20}}$.
First, calculate $(1 + 0.05)^{20}$. Using the formula $a^n$, where $a = 1.05$ and $n = 20$, we have $(1.05)^{20}\approx2.653297705$.
Then, $P=\frac{30000}{2.653297705}\approx11306$.
# Answer:
$11306$