Answer the following questions assuming, where necessary, the interest rate is $10\%.$

$($i$)$ A couple wishes to save $$250,000$ over the next $18$ years for their child's education.

What annual amount must they deposit at the end of each year?

$($ii$)$ What return do you earn if you pay $$22,470$ for a stream of $$5,000$ payments lasting

ten years? What does it mean if you pay less than $$22,470$ for the stream? More than

$$22,470?$

$($iii$)$ A company is planning to set aside money to repay $$150$ million in bonds that will

be coming due in $8$ years. How much money would the company need to set aside at

the end of each year for the next $8$ years to repay the bonds when they come due?

How would your answer change if the money were deposited at the beginning of

each year?