The present value (PV) of an immediate annuity can be calculated using the formula for the present value of an annuity due, which takes into account the fact that payments are made immediately upon inception and then increase by 1 each year for four years. The formula to calculate the present value of an annuity due is:

[ PV = \frac{PMT \times \frac{1 - (1 + i)^{-n}}{i} \times (1 + i)^n - 1} ]

Where: - PMT is the individual payment amount. - i is the interest rate per period. - n is the number of periods.

Given that the first payment is received immediately and each subsequent payment increases by 1, we have PMT = 1 for the first year, PMT = 2 for the second year, PMT = 3 for the third year, and PMT = 4 for the fourth year. The interest rate i = 5% and the number of periods n = 4.

Let's calculate the present value for each year and sum them up to get the total present value:

Year 1: ( PV_1 = \frac{1 \times (1 + 0.05)^{-1}}{0.05} \times (1 + 0.05)^1 - 1} \approx 1.9048 ) Year 2: ( PV_2 = \frac{2 \times (1 + 0.05)^{-2}}{0.05} \times (1 + 0.05)^2 - 1} \approx 3.6545 ) Year 3: ( PV_3 = \frac{3 \times (1 + 0.05)^{-3}}{0.05} \times (1 + 0.05)^3 - 1} \approx 5.4818 ) Year 4: ( PV_4 = \frac{4 \times (1 + 0.05)^{-4}}{0.05} \times (1 + 0.05)^4 - 1} \approx 7.1773 )

Total Present Value: ( PV_{total} = PV_1 + PV_2 + PV_3 + PV_4 \approx 1.9048 + 3.6545 + 5.4818 + 7.1773 \approx 18.1184 )

So, the present value of the immediate annuity with increasing payments is approximately $18.12.