What is the discounted payback period for these cash flows if the initial cost is $11,800?

C) initial cost = 11800

This time it will take you full 4 years

5300/1.13^4 = 3250.59

14855.44 - 8800 = 3055.44

cash required in year 4 = 3250.59 - 3055.44 = 195.15

time required in year 4 = 195.15 / 3250.59 = 0.06

Discounted payback period = year 1 + year 2 + year 3 + 0.06 = 3.06 years