Question

You receive a ​$11 comma 000 check from your grandparents for graduation. You decide to save it toward a down payment on a house. You invest it earning 9​% per year and you think you will need to have ​$22 comma 000 saved for the down payment. How long will it be before the ​$11 comma 000 has grown to ​$22 comma 000 ​?

Answer 1

Answer:

• 7 years and 9 months.

Explanation:

You can calculate the number of years needed to the $11,000 grow to $22,000, using the compound interest formula, with:

• Present value or investment: $11,000

• APR: 9%

• Assume monthly compound interest: r = 9%/12 = 0.09/12 = 0.0075

• Future value: $22,000

The equation is:

        $\text{Future value}=Investment\times (1+r)^t$

Where r is the monthly compound interest (r = 0.0075) and t is the number of months.

Substitute and solve for t:

       $\ 22,000=\ 11,000\times (1+0.0075)^t$

       $2=(1.0075)^t\\\\t=\dfrac{\log 2}{\log 1.0075}\approx92.8months\\\\\\t=93/12=7.75years=7years+9months$