Assume that your parents wanted to have $$100,000$ saved for university 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 $6\mathrm{.}5\%$ 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 $$140,000$ saved, just in case, how much would they have to save each year to reach their new goal?