How long does a $4000 investment take to earn $720 interest if the interest rate is 6% per year?

1 Answer
Jul 13, 2016

See the explanation.
As the answer for simple interest is a whole number I suspect this is the type of interest that applies.

3 years

Explanation:

#color(red)("You do not state the type of interest")#

#color(blue)("Simple interest")#

#"The interest obtained for each year " -> 6/100xx$4000=$240#

#"The time spans " ($720)/($240) =color(blue)(3" years")#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("Compound interest")#

The final sum in the account would be #$4000+$720=$4720#

The standard form equation is: #P(1+x/100)^n#

So we have: #4000(1+6/100)^2=4720#

#(106/100)^n=4720/4000#

Taking logs

#nlog_10(106/100)=log_10(4720/4000)#

#n=log_10(4720/4000)-:log_10(106/100)#

#n=(log_10(1.18))/(log_10(1.06)) color(blue)(~~2.84 " years to 2 decimal places")#