You invest $6500 into a mutual fund that is expected to earn 6% per year. how long will it take the fund to be worth $13,000?

This is a compound interest problem so you cannot use the simple interest formula. Effectively the total amount is being compounded each year by 6%. There is a formula for compound interest but in this simple example you can work this out recursively.

year 1 = 6500
year2 = 6500*1.06 = 6890
year3 = 6890*1.06 = 7303
year4 = 7303*1.06 = 7741..
etc
year12 = 11604*1.06 = 12338 

It will take about 12 years to worth 12 years to worth $13,000

Compound interest

The formula for calculating compound interest is expressed as:

Given the following parameters:

A = $13,000P = $6500r = 6% = 0.06

Substitute into the formula

Hence it will take about 12 years to worth 12 years to worth $13,000

Learn more on compound interest here; link

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