Question

Josh's grandparents put $3,000 into a college savings account when he was born. The account earns 6% interest per year. How long will it take before he has $15,000?

Answer 1

Answer:

Therefore it will take 28 years.

Step-by-step explanation:

To find the years, we use the following formula,

$A=P(1+r)^n$

A= Total balance after n years

P= Initial amount.

r= Rate of interest per year.

n = Time in years.

Given that, Josh's grandparents put $3,000 into a college saving account when he was born. The account earn 6% interest per years.

Here A=$15,000,P=$3,000, r=6%=0.06 ,n=?

$\therefore 15,000=3,000(1+0.06)^n$

$\Rightarrow (1.06)^n=\frac{15,000}{3,000}$

$\Rightarrow (1.06)^n=5$

Taking ln both sides

$\Rightarrow ln(1.06)^n=ln(5)$

$\Rightarrow n=\frac{ln(5)}{ln(1.06)}$

$\Rightarrow n\approx 28$

Therefore it will take 28 years.