To find the total amount Ravi has to pay after one year with the given conditions, we need to use the formula for compound interest. Compound interest is calculated using the formula:

\(A = P \left(1 + \frac{r}{n}\right)^{nt}\)

where:

• \(A\) is the future value of the investment/loan, including interest.
• \(P\) is the principal investment/loan amount (₹16,000).
• \(r\) is the annual interest rate (decimal) (20% or 0.20).
• \(n\) is the number of times that interest is compounded per unit year (quarterly compounding means \(n = 4\)).
• \(t\) is the time the money is invested/borrowed for in years (1 year).

Substituting the given values into the formula, we get:

\(A = 16000 \left(1 + \frac{0.20}{4}\right)^{4 \times 1}\)

Simplifying further:

\(A = 16000 \left(1 + 0.05\right)^{4}\)

\(A = 16000 \left(1.05\right)^{4}\)

Calculating the power of 1.05 raised to 4:

\((1.05)^4 = 1.21550625\)

Now, substitute back to find A:

\(A = 16000 \times 1.21550625\)

Calculate the final amount:

\(A \approx 19448.10\)

Therefore, the amount that Ravi has to pay after one year is ₹19,448.10, which matches the first option.