A family spent $7845 on vacations this year. If this family decreases the amount it spends on vacations by 2.75% every year, what is the amount the family will spend on vacations in 5 years?

$6,824.03 is the amount the family will spend on vacations in 5 years

Step-by-step explanation:

The formula A = P(1 + r)^n is appropriate in this problem, with the understanding that A represents the amount the family will spend on vacations in n years and P is the current spending amount.  Then:

A = ($7,845)(1 - 0.0275)^5, where we use -0.0275 to indicate that the amount DECREASES by 2.75% annually.  Simplifying this formula, we get:

A = ($7,845)(0.9725)^5, whose value to the nearest cent comes out to:

A = $6,824.03 is the amount the family will spend on vacations in 5 years.  

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