how much money should be deposited today in a...
how much money should be deposited today in an account that earns 4.5% compounded monthly so that it will accumulate to $13,000 in 3 years? click the icon to view some finance formulas. the amount of money that should be deposited is $ (round up to the nearest cent.)
Answer
# Explanation:
## Step1: Identify the compound - interest formula
The compound - interest formula for present value $P$ is $P=\frac{A}{(1 + \frac{r}{n})^{nt}}$, where $A$ is the future value, $r$ is the annual interest rate (in decimal form), $n$ is the number of times compounded per year, and $t$ is the number of years.
## Step2: Convert the given values to the appropriate form
We have $A = 13000$, $r=0.045$ (since $4.5\%=0.045$), $n = 12$ (compounded monthly), and $t = 3$.
## Step3: Substitute the values into the formula
$P=\frac{13000}{(1+\frac{0.045}{12})^{12\times3}}$.
First, calculate the value inside the parentheses: $\frac{0.045}{12}=0.00375$, and $1+\frac{0.045}{12}=1.00375$.
Then, calculate the exponent: $12\times3 = 36$.
So, $(1.00375)^{36}\approx1.143204$.
Finally, $P=\frac{13000}{1.143204}\approx11371.53$.
# Answer:
$11371.53$