Question

Wade's homeowner's insurance costs $650 a year. His first payment is $140. Then each payment is 20% of what he owes after the first payment. How much is each remaining payment?

Answer 1

Wade's homeowner's insurance costs $650 a year.

Since his first payment is $140, then the amount remaining after the first payment will be $650 - $140 = $510.

If each payment is 20% of what he owes after the first payment, this implies that his second payment will be

`(20)/(100)*510=102`

The second payment will be $102

The amount remaining after the second payment will be $510 - $102 = $408

Now, to know the next remaining payment, we have to calculate the ratio of the amount remaining after the first and the second payment, that is

`(510)/(408)=1.25`

Therefore, we shall generate the next remaining payment by multiplying the previous remaining payment by 1.25. This yields the sequence below

$510, $408, $326.4, $261, $208.896, $167.1168....................$1.541