Lucy invested $10,000 in a new mutual account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?
Great observation! Yes, because the order in which we multiply doesn't matter (this is the Commutative Property), we can find the final value by multiplying the product of the multipliers by the original value :)
In other words,
Final value = [product of multipliers]*[original value]
While we can multiply the values in any order, that's not necessarily the best approach. It looks like Chitrabhanu provides a straight forward way to do the calculation efficiently. First they multiplied
1.1*0.9 = .99
then
1.05*10000 = 10500
leaving us with
0.99*10500
Instead of finding this product directly, it's a faster calculation if we recognize that the product is 0.01 (1%) less than 10500. One percent of 10500 = 105, so
3 Explanations