# What rate is necessary to double an investment of $4000 in 10 years?

##### 2 Answers

Simple interest: 10%

Compound interest: 7.17735%, nearly.

#### Explanation:

The percentage interest p for simple interest is given by

4000(1+(10)(p/100))=8000 giving p = 10%.

For compound interest p, the equation to be solved is

So,

This gives p =7.17735%, nearly.

Simple interest rate

Coumpound interest

#### Explanation:

The question does not indicate whether the interest is simple or compound interest.

Let's consider both..

The formula to calculate **SIMPLE interest:**

For the investment to double, the amount of interest has to be $4000.

($4000 invested + $4000 interest = $8000 in total.)

Making R the subject gives

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

If the interest is **compounded annually** , the formula is

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

In reality, neither of these is practical.

Investments do not earn simple interest.

Interest is usually compounded monthly, even daily, but rarely annually.

But the question leads to some nice math calculations.......