Since 2004, the amount of money spent at restaurants in a certain country has increased at a rate of 7% each year. In 2004, about $290 billion was spent at restaurants. If the trend continues, about how much will be spent at restaurants in 2018?
Since 2004, the amount of money spent at restaurants in a certain country has increased at a rate of 7% each year. In 2004, about $290 billion was spent at restaurants. If the trend continues, about how much will be spent at restaurants in 2018?
2.9E8 * (1 + .07)^(2018 - 2004)
sorry ... that should be ... 2.9E11 * (1 + .07)^(2018 - 2004)
To calculate the amount of money that will be spent at restaurants in 2018 based on the given information, we need to use the compound interest formula.
The compound interest formula is given by:
A = P(1 + r/n)^(n*t)
Where:
A = the final amount
P = the initial amount
r = the annual interest rate (expressed as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case, the initial amount spent at restaurants in 2004 is $290 billion, the annual interest rate is 7% (or 0.07 as a decimal), and the number of years is 2018 - 2004 = 14 years.
Substituting the given values into the formula, we have:
A = 290 billion * (1 + 0.07/1)^(1*14)
Simplifying the equation, we get:
A = 290 billion * (1.07)^14
Using a calculator to evaluate this expression, we find:
A ≈ $613.12 billion
Therefore, if the trend continues, about $613.12 billion will be spent at restaurants in 2018.