debra needs to invest to help with her childs college fund. how much would she have to invest to have…

Explanation:

Step1: Identify the compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $A$ is the final amount, $P$ is the principal amount (initial investment), $r$ is the annual interest rate (in decimal form), $n$ is the number of times interest is compounded per year, and $t$ is the number of years. We need to solve for $P$, so we can rewrite the formula as $P=\frac{A}{(1 +\frac{r}{n})^{nt}}$.

Step2: Convert the given values to the appropriate form

The annual interest rate $r = 2.19%=0.0219$, the number of times compounded per year $n = 4$ (quarterly compounding), the number of years $t = 14$, and the final amount $A=$98700$.

Step3: Calculate the exponent

First, calculate $nt$: $nt=4\times14 = 56$. Then, calculate $1+\frac{r}{n}$: $1+\frac{0.0219}{4}=1 + 0.005475=1.005475$.

Step4: Calculate the denominator

Calculate $(1+\frac{r}{n})^{nt}=(1.005475)^{56}$. Using a calculator, $(1.005475)^{56}\approx1.36777$.

Step5: Calculate the principal amount

Now, find $P$: $P=\frac{A}{(1+\frac{r}{n})^{nt}}=\frac{98700}{1.36777}\approx72159$.

Answer:

$72159$