Question

Thor invests some $20,000 in an account earning 8% interest each year. Write an inequality that could be used to determine the number of years, n, that it will take for the account to have at least $27,000.

Answer 1

The required inequality is
`27000\leq 20000(1+0.08)^n`.

Explanation:

The principle amount is $20,000.

The interest rate is 8% per year.

The formula of compound interest annually is

`A=P_0(1+r)^n`

Where, P₀ is principle amount, r is rate and n is time in years.

The amount is

`A=20000(1+0.08)^n`

We need the amount at least $27,000. It means $27000 or more than $27,000.

`27000\leq 20000(1+0.08)^n`

`27\leq 20(1+0.08)^n`

`n\geq 3.899`

Therefore the required inequality is
`27000\leq 20000(1+0.08)^n`.