You have borrowed money from a bank which gives two equal options for repayment. Option $1$ involves paying $$5,000$ at the end of each year for $10$ years at annual interest rest of $12\%.$ How long would Option $2$ be if you have to pay $$1200$ at the annual interest rate of $13\%?$ Please assume the first payment is being made a year from today.

Group of answer choices

$5$ years

$20$ years

$8$ years

$11$ years