#### Explanation:

The formula for compound interest is $A = P {\left(1 + i\right)}^{n}$.
$A$ represents the final amount that that account has grown to,
$P$ represents the starting amount of money (usually called the principal or present value),
$i$ represents the interest rate per compound, and
$n$ represents the number of compounds.

In this question, $A = 20 000$, $P$ is the unknown value, $i$
is $\frac{0.07}{4}$ since there are 4 compounding periods per year when the interest is compounded quarterly, and $n$ is 15.

$A = P {\left(1 + i\right)}^{n}$
$20 000 = P {\left(1 + \frac{0.07}{4}\right)}^{15}$
$20 000 = P {\left(1 + 0.0175\right)}^{15}$
$20000 = P {\left(1.0175\right)}^{15}$
$20000 = P \left(1.297227864\right)$

Dividing both sides by (1.297227864) gives us
$\frac{20000}{1.297227864} = P$

The answer is $P = 15417.49$

Thus, $15 417.49 will grow to$20 000 if interests is 7% compounded quarterly for 15 quarters.