Question

How long will it take $2,000 to reach $3,000 when it grows at 12 percent per year? (Do not round intermediate calculations. Round "months" to 1 decimal place.)

Answer 1

4.2 years

Explanation:

assuming simple interest (see attached graphic), the following formula applies.

A = P [ 1 + (rt) ] where,

A = final amount = $3,000

P = Principal Amount = $2,000

r = annual rate = 12% = 0.12

t = time in years

Substituting the above values into the formula gives,

3000 = 2000 [ 1 + (0.12)(t) ] (divide both sides by 2000)

3000/2000 = 1 + 0.12t

(3/2) = 1 + 0.12t (subtract 1 from both sides and rearrange)

0.12t = (3/2) - 1

0.12t = (1/2) (note 1/2 = 0.5)

0.12t = 0.5 (divide both sides by 0.12)

t = 0.5 / 0.12

t = 4.166666666667

t = 4.2 years (1 dec. pl)

Answer 2

It is going to take 4.2 years for $2,000 to reach $3,000.

Explanation:

This is a simple interest problem.

The simple interest formula is given by:

`E = P*I*t`

In which E are the earnings, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

`T = E + P`.

In this problem, we have that:

`P = 2000, I = 0.12`

We want to find t when
`T = 3000`

So

`T = E + P`.

`3000 = E + 2000`

`E = 1000`

-----------

`E = P*I*t`

`1000 = 2000*0.12t`

`0.12t = 0.5`

`t = (0.5)/(0.12)`

`t = 4.2`

It is going to take 4.2 years for $2,000 to reach $3,000.