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

Answer:

n = 43.6673555

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

Explanation:

we solve for time of a future lump-sum:

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

we use logarithmics properties:

$(1+r)^n = FV/PV\\log_{1+r}FV/PV = n\\n = \frac{log FV/PV}{log(1+r)}$

PV 49,000

FV 98,000

rate 1.6%

$n = \frac{log 98,000/49,000}{log(1+0.016)}$

n = 43.6673555