Question

Suppose that real GDP per capita in the United States is $49,000. If the long-term growth rate of real GDP per capita is 1.6% per year, how many years will it take for real GDP per capita to reach $98,000? Instructions: Enter your answer as a whole number. years

Answer 1

Using the rule of 70, it will take approximately 44 years for the real GDP per capita in the United States to double from $49,000 to $98,000 at a 1.6% annual growth rate.

Step-by-step explanation:

To determine how many years it will take for real GDP per capita in the United States to grow from $49,000 to $98,000 at an annual growth rate of 1.6%, we use the rule of 70. The rule of 70 is a way to estimate the number of years required to double an investment at a given annual rate of return. By dividing 70 by the growth rate, you get the approximate number of years to double.

Years to double = 70 / growth rate

In this case:

Years to double = 70 / 1.6 = 43.75 years

Since we're looking for the number of years it will take to double from $49,000 to $98,000 and considering we should round to the nearest whole number:

Years to double = 44 years

Answer 2

n = 43.6673555

it will take 43.67 year to achice a real GDP of 98,000

Step-by-step explanation:

we solve for time of a future lump-sum:

`PV (1+r)^n = FV\\(1+r)^n = FV / PV\\`

we use logarithmics properties:

`(1+r)^n = FV/PV\\log_(1+r)FV/PV = n\\n = (log FV/PV)/(log(1+r))`

PV 49,000

FV 98,000

rate 1.6%

`n = (log 98,000/49,000)/(log(1+0.016))`

n = 43.6673555