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

Therefore it will take 28 years.

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=(15,000)/(3,000)`

`\Rightarrow (1.06)^n=5`

Taking ln both sides

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

`\Rightarrow n=(ln(5))/(ln(1.06))`

`\Rightarrow n\approx 28`

Therefore it will take 28 years.