1. The problem states that $1000$ is deposited in a savings account with an annual interest rate of $12.2\%$, compounded quarterly, for $18$ months. We are asked to find the annual percentage rate (APR).\n\n2. First, recall that APR is the yearly interest rate without considering compounding within the year. The nominal annual interest rate given is $12.2\%$, so the APR is $12.2\%$.\n\n3. However, often people confuse the nominal APR with the effective annual rate (EAR), which accounts for compounding. Let's find the EAR to see the actual annual interest earned.\n\n4. The formula for the EAR when interest is compounded $n$ times per year is:\n$$EAR = \left(1 + \frac{r}{n}\right)^n - 1$$\nwhere $r = 0.122$ (annual nominal rate as a decimal) and $n = 4$ (quarterly compounding).\n\n5. Substitute the values:\n$$EAR = \left(1 + \frac{0.122}{4}\right)^4 - 1 = \left(1 + 0.0305\right)^4 - 1$$\n\n6. Calculate:\n$$EAR = (1.0305)^4 - 1$$\n$$EAR \approx 1.1275 - 1 = 0.1275$$\n\n7. Convert to percentage:\n$$EAR \approx 12.75\%$$\n\n8. The APR is the nominal rate, $12.2\%$. The effective annual rate (EAR), which accounts for compounding, is approximately $12.75\%$. Note the question asks specifically for APR, which remains $12.20\%$.\n\nFinal answer: $\boxed{12.20\%}$