Final answer:
To calculate the amount you should pay for the annuity, use the present value formula for an annuity with the given annual payments, interest rate, and number of periods.
Step-by-step explanation:
To calculate how much you should pay for the annuity, you can use the formula for the present value of an annuity. The present value of an annuity is the current worth of a series of future cash flows. In this case, the future cash flows are the annual payments of $1400 over 18 years. The formula for present value of an annuity is:
PV = PMT x ((1 - (1 + r)⁻ⁿ) / r)
In this formula, PV represents the present value, PMT represents the annual payment, r represents the interest rate per period (divided by 100 to convert it to decimal form), and n represents the number of periods. Plugging in the values from the question:
PV = $1400 x ((1 - (1 + 0.0632)^-18) / 0.0632)
Calculating this expression gives approximately:
PV ≈ $16,656.34