Question

Leslie wants to invest $3,800.00 in a savings account that pays 4.8% simple interest.

How many years will it take for this investment to triple in value? Round your answer to the nearest tenth of a year.

It will take _______ years for this investment to triple in value.

Answer 1

It will take 41.7 years for this investment to triple in value.

Explanation:

Here is the formula for simple interest

`A=P(1+rt)`

Lets solve for
`t`.

Divide both sides by
`P`.

`(A)/(P)=rt+1`

Subtract 1 from both sides.

`(A)/(P)-1=rt`

Divide both sides by
`r`.

`((A)/(P)-1)/(r) =t`

To write
`-1` as a fraction with a common denominator, multiply by
`(P)/(P)` .

`((A)/(P)-1*(P)/(P))/(r) =t`

`((A)/(P)*(-P)/(P))/(r) =t`

Combine the numerators over the common denominator.

`((A-P)/(P) )/(r) =t`

Multiply the numerator by the reciprocal of the denominator.

`t=(A-P)/(Pr)`

We are given

`P=3800\\r=0.048`

We need to find what amount is triple his money.

`3800*3=11400`

`A=11400`

Substitute our numbers into the equation for
`t`.

`t=(11400-3800)/(3800*0.048)`

Factor 3800 out of 11400.

`t=(3800*3-3800)/(3800*0.048)`

Factor 3800 out of −3800.

`t=(3800*3-3800*-1)/(3800*0.048)`

Factor 3800 out of
`3800*3-3800*-1`.

`t=(3800*(3-1))/(3800*0.048)`

Cancel the common factor of 3800.

`t=(3-1)/(0.048)`

Simplify.

`t=(2)/(0.048)`

`t=41.666`

Merry Christmas!