Question

Question: How long does it take an investment to quadruple in value if it earns 4% simple interest per year?

(answer algebraically please)

Answer 1

It takes 75 years for the investment to quadruple in value

Explanation:

Simple Interest

This is a simple interest problem.

The simple interest formula is given by:

`E = P*I*t`

In which E is the amount of interest earned, 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 question:

4% simple interest per year, so I = 0.04.

Quadruple:

t when T = 4P.

The interest earned is:

`T = E + P`

`4P = E + P`

`E = 3P`

Now we find the time.

`E = P*0.04*t`

`3P = P*0.04*t`

`0.04t = 3`

`t = (3)/(0.04)`

`t = 75`

It takes 75 years for the investment to quadruple in value