Calculate by how much AND AT WHAT COMPOUND ANNUALIZED RATE U

Calculate by how much, AND AT WHAT COMPOUND ANNUALIZED RATE, U.S. per capita real income has increased between the first quarter of 1996 and today.

If this growth persists for another 20 years what will U.S per capita real GDP be?

Solution

As per St. Louis FRED data,

US per capita real income, Q1 1996 = $27,608

US per capita real income, Nov 2015 (Latest available data) = $38,509

If compound annualized rate be r,

$27,608 x (1 + r)¹⁹ = $38,509

(1 + r)¹⁹ = 38,509 / 27,608 = 1.3948

Taking 19th-root in each side,

1 + r = 1.0183

r = 1.0183 - 1 = 0.0183, or 1.83%

If growth persists at 1.83%, after 20 years, per capita real GDP = $38,509 x (1.0183)²⁰ = $38,509 x 1.4372

= $55,344.84