# How long will it take to earn $1800 in interest if $6000 is invested at a 6% annual interest

###### Question:

## Answers

Total interest will $1800 after 5 years.

Step-by-step explanation:

It is given that the principle amount is $6000.

Rate of interest rate is 6% per annum.

Total interest is $1800.

Formula for simple interest is

[tex]I=\frac{P\times r\times t}{100}[/tex]

Where, P is principle, r is rate of interest in percent and t is time in years.

Substitute P=6000, r=6 and I=1800 in the above formula.

[tex]1800=\frac{6000\times 6\times t}{100}[/tex]

[tex]1800=\frac{36000t}{100}[/tex]

[tex]1800=360t[/tex]

Divide both sides by 360.

[tex]\frac{1800}{360}=t[/tex]

[tex]5=t[/tex]

Therefore the total interest will $1800 after 5 years.

b. 5 years

Step-by-step explanation:

It will take 5 years.

Step-by-step explanation:

Let's find how long it will take, but first let's understand the equation.

For simple interest, we use the equation:

T=(1/R)*(((A+B)/B)-1) where,

A= interest amount

B=invested money

R=interest rate (in decimal form)

T=time

Because we want to earn $1800 in interest, then A=1800.

Because we invested $6000, then B=6000.

Because we are investing under an interest rate of 6%, then R=0.06.

'How long will it take' means that T= not given, but its value is in 'years', since an annual rate was given.

Using the equation for simple interest we write:

T=(1/0.06)*(((1800+6000)/6000)-1), the solution is then:

T=5; remember, because is an annual rate, T solution means 5 years.

idk

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