Question

The 1997 a value of an object was $5000. In 2012, it was worth $9500. The annual percent growth has been constant. What is the annual percent growth?

Answer 1

Annual percent growth is 4.37 %

Solution:

The increasing function is given as:

$y = a(1+r)^t$

Where,

y is future value

a is initial value

r is growth rate

t is number of years

From given,

a = 5000

y = 9500

t = 1997 to 2012 = 15 years

r = ?

Substituting the values we get,

$9500 = 5000(1+r)^{15}\\\\(1+r)^{15} = 1.9\\\\Take\ \frac{1}{15}th\ power\ on\ both\ sides\\\\1+r = (1.9)^{\frac{1}{15}}\\\\1+r = 1.04367\\\\r = 1.04367 - 1\\\\r = 0.04367\\\\In\ percentage,\\\\r = 0.04367 \times 100 \%\\\\r = 4.367 \% \approx 4.37 \%$

Thus annual percent growth is 4.37 %