A deposit earns 26% per annum, compounded annually. At the end of which year does the amount standing in the account first exceed four times the sum deposited?

At 26% the money multiplies by 1.26 each year, and $(1.26{)}^3=2.0004$ — it just doubles every 3 years. Doubling twice quadruples it, so $(1.26{)}^6=4.0015$ clears four times in the 6th year, while $(1.26{)}^5=3.1758$ is still short. (Year 4 simply echoes the multiple asked for. Under simple interest the money would need 300%/26% ≈ 11.5, i.e. 12 years, to reach four times — compounding gets there in half that.)