Answer:
$18,034.40
Step-by-step explanation:
We will use the compound interest formula:
[tex]A_{final}=A_{initial}(1+\frac{r}{n})^{nt}[/tex]
Our final amount is $22,000, t = 4, r = 5% = 0.05 (because 5/100=0.05) and n=4 since it's compounded quarterly this means that it happens four times in one year. By plugging in your values you obtain:
[tex]22000=A_{initial}(1+\frac{0.05}{4})^{4(4)}\\\\22000=A_{initial}(1+0.0125)^{16}\\\\22000=A_{initial}(1.0125)^{16}\\\\A_{initial}=\frac{22000}{1.0125^{16}}\\\\A_{initial}=18034.40[/tex]
Therefore, you would need to place an initial amount of $18,034.40 in order to accumulate $22,000 based on the parameters given.
