Question

how much money should be deposited today in an account that earns 2.5% compounded monthly so that it will accumulate to $13,000 in 2 years? click the icon to view some finance formulas. the amount of money that should be deposited is $ (round up to the nearest cent.)

Explanation:

Step1: Identify the compound - interest formula

The compound - interest formula for present value is $P = \frac{A}{(1+\frac{r}{n})^{nt}}$, where $A$ is the future value, $P$ is the present value (the amount to be deposited today), $r$ 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 $A=\$13000$, $r = 0.025$ (since $2.5\%=0.025$), $n = 12$ (compounded monthly), and $t = 2$ years.

Step3: Substitute the values into the formula

$P=\frac{13000}{(1 +\frac{0.025}{12})^{12\times2}}$.
First, calculate the value inside the parentheses: $\frac{0.025}{12}\approx0.0020833$, and $1+\frac{0.025}{12}=1.0020833$.
Then, calculate the exponent: $12\times2 = 24$.
So, $(1.0020833)^{24}\approx1.0511619$.
Finally, $P=\frac{13000}{1.0511619}\approx12367.04$.

Answer:

$12367.04$