1. you want $25,000 in 7 years. the account pays 5.2% annual interest compounded monthly. how much must you…

Explanation:

Step1: Identify the formula

The future - value of an ordinary annuity formula is $FVA = P\times\frac{(1 + \frac{r}{n})^{nt}-1}{\frac{r}{n}}$, where $FVA$ is the future value of the annuity, $P$ is the payment per period, $r$ is the annual interest rate (in decimal), $n$ is the number of compounding periods per year, and $t$ is the number of years. We need to solve for $P$, so $P=\frac{FVA\times\frac{r}{n}}{(1 + \frac{r}{n})^{nt}-1}$.

Step2: Convert the given values to the appropriate form

Given $FVA = 25000$, $r=0.052$ (since $5.2%=0.052$), $n = 12$ (compounded monthly), and $t = 7$. First, calculate $(1+\frac{r}{n})^{nt}=(1+\frac{0.052}{12})^{12\times7}$. $1+\frac{0.052}{12}=1+\frac{13}{3000}=\frac{3000 + 13}{3000}=\frac{3013}{3000}$. $(1+\frac{0.052}{12})^{84}=(\frac{3013}{3000})^{84}$. Using a calculator, $(\frac{3013}{3000})^{84}\approx1.4447$. $\frac{r}{n}=\frac{0.052}{12}\approx0.00433$.

Step3: Substitute values into the formula for $P$

$P=\frac{25000\times0.00433}{1.4447 - 1}$. $25000\times0.00433 = 108.25$. $1.4447-1 = 0.4447$. $P=\frac{108.25}{0.4447}\approx243.42$.

Answer:

$$243.42$