tammy is going to invest to help with a down payment on a home. 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 want 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 $r = 1.62%=0.0162$, the number of times compounded per year $n = 4$ (compounded quarterly), the number of years $t = 10$, and the final amount $A=$24700$.

Step3: Substitute the values into the formula

$P=\frac{24700}{(1+\frac{0.0162}{4})^{4\times10}}$. First, calculate the value inside the parentheses: $\frac{0.0162}{4}=0.00405$, and $1+\frac{0.0162}{4}=1 + 0.00405=1.00405$. Then, calculate the exponent: $4\times10 = 40$. So, $(1.00405)^{40}\approx1.17027$.

Step4: Calculate the principal amount

$P=\frac{24700}{1.17027}\approx21106$.

Answer:

$$21106$