Answer: 528
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Explanation:
The value drops by 30% meaning that it keeps 70% of its value (the two percentages add to 100%)
We start off at $2200. We apply 70% to this current value to get next year's value.
After 1 year, the value is 2200*0.7 = 1540 telling us that 70% of 2200 is 1540.
After 2 years, the value is 1540*0.7 = 1078
After 3 years, the value is 1078*0.7 = 754.6
After 4 years, the value is 754.6*0.7 = 528.22
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A shortcut is to use the formula
A = P*(1+r)^n
with A as the final amount, P is the starting amount, r as the growth rate, and n as the number of years.
In this case, P = 2200, r = -0.30 and n = 4. The negative growth rate is another way of saying "value drops". Note how I represent 30% as 0.30; therefore a drop of 30% is -0.30
With all those values in mind, let's plug them into the formula
A = P*(1+r)^n
A = 2200*(1+(-0.3))^4
A = 2200*(1-0.3)^4
A = 2200*(0.7)^4 .... see note below
A = 2200*0.2401
A = 528.22
Whichever method you use, the value is 528.22 dollars which rounds to 528 dollars (when rounding to the nearest whole dollar)
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note: In this line, the (0.7)^4 term represents repeated multiplications of 0.7; specifically exactly four copies of 0.7 are multiplied together. This is a condensed format as opposed to calculating the value each year as done at the top of the problem. So in a sense, we apply 70% to each current value to get the next value. This formula is especially handy if n is large.
