GDP per capita in the U.S. was approximately $41,000 in 2005, what will it be in the year 2015 in GDP per capita grows each year by
A) 0%
B) 2%
C)4%
Use algebra.
a) 41,000
b) 41,000*((1.02)^10)
c) 41,000*((1.04)^10)
To find the GDP per capita in the year 2015 given different growth rates, we can use the formula for compound interest:
Future Value (FV) = Present Value (PV) * (1 + r)^n
Where:
FV = future value
PV = present value
r = growth rate per period
n = number of periods
For each scenario, we can plug in the values and calculate the future GDP per capita in 2015.
a) 0% growth rate:
In this case, the GDP per capita remains the same each year. Therefore, the future GDP per capita in 2015 will be the same as in 2005, which is $41,000.
b) 2% growth rate:
Plugging the values into the formula, we get:
FV = $41,000 * (1 + 0.02)^10
FV = $41,000 * (1.02)^10
c) 4% growth rate:
Using the same formula, we have:
FV = $41,000 * (1 + 0.04)^10
FV = $41,000 * (1.04)^10
To calculate the values for options b) and c), we can simplify by raising the growth rate to the power of 10.
Now that we have set up the formulas, we can calculate the future GDP per capita in 2015 for each growth rate:
a) $41,000
b) $41,000 * (1.02)^10
c) $41,000 * (1.04)^10
Using algebraic notation, the answers for the future GDP per capita in 2015 are as follows:
a) $41,000
b) 41,000 * (1.02)^10
c) 41,000 * (1.04)^10