Assume that your parents wanted to have $$160,000$ saved for college by your $18$ th birthday and they started saving on your first birthday. They saved the same amount each year on your birthday and earned $12\mathrm{.}5\%$ per year on their investments.

a$.$ How much would they have to save each year to reach their goal?

b$.$ If they think you will take five years instead of four to graduate and decide to have $$200,000$ saved just in case, how much would they have to save each year to reach their new goal?

a$.$ How much would they have to save each year to reach their goal?

To reach the goal of $$160,000,$ the amount they have to save each year is $$.($Round to the nearest cent.$)$