The rate of return for doubling money every 10 years depends on the type of compounding used; the more often interest is compounded, the less the rate of interest needed to achieve the same results. Compounded interest can be made at specified intervals or continuously. The type of compounding will affect the amount of interest you earn on your initial investment.

## Compounding

The basics of compounding will dictate how much money you earn in any investment. Compounding is the principle of earning interest on the interest you have already earned. If you invest $100 at 5 percent compounded yearly for three years, that means that you will earn 5 percent on the $100 in year one and it will be deposited in the account at the end of the year. For year two, you will earn 5 percent on $105. The additional $5 comes from the interest earned in year one. At the end of year two you will have $110.25. At the end of year three, your account will have $115.76. If the account did not have yearly compounding, earning interest on interest, then the total of your account would only be $115.00 at the end of three years.

## Yearly Compounding

When your money is invested at a rate of 7.178 percent for 10 years, it will be doubled at the end of those 10 years if interest is compounded yearly. The equation to find this is:

FV = PV (1 + i) ^ t

Where: FV = future value PV = present value i = rate of interest per year t = time in years

There is no easy way to solve for i in this equation, so using trial and error you can find that 7.178 percent is the closest value of i. When the present value is set at $5,000 and the future value is set at $10,000 with a time of 10 years, using iterations you will find that 7.178 percent will give you $10,000.61 after 10 years of yearly compounding.

## Monthly Compounding

When your money is invested at a rate of 6.952 percent for 10 years, it will be doubled at the end of those 10 years if interest is compounded monthly. The equation to find this is:

FV = PV(1 + i/n) ^ (t x n)

Where: FV = future value PV = present value i = rate of interest per year t = time in years n = 12

The value n is a set value of 12 because compounding is done monthly and there are 12 months in a year. Using trial and error to solve for i, you will find that a rate of 6.952 percent will give you $10,000.47 after 10 years of monthly compounding.

## Continuous Compounding

When your money is invested at a rate of 6.932 percent for 10 years, it will be doubled at the end of those 10 years if interest is continuously compounded. The equation to find this is:

FV = PV x e ^ (i x t)

Where: FV = future value PV = present value i = interest rate t = years

There is no easy way to solve for i, so you find it by using trial and error. With a present value of $5,000 and a future value of $1,000, using iterations you will find that a rate of 6.932 percent after 10 years will give you a value of $10,000.53 after 10 years.