You have the money in an account at 6% interest, compounded quarterly. To the nearest year, how long will it take for your money to double? 

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durbanville's profile pic

durbanville | High School Teacher | (Level 2) Educator Emeritus

Posted on

You need to use the formula for compound interest which is

`A= P(1+r/100)^(n)`

A is the future value - in our case it is double what we started with.

P is the current value of the money (funds) for investment.

r (or i) is the rate of interest and is divided by 100 because it is expressed as a percentage which is any amount out of 100.

n is the number of years we are investing for.

The above formula is the standard formula and is used as is when compounding annually (once a year)Care to adjust the formula to allow for the quarterly compounding by dividing`r/100` by 4. If it was compounded annually you would divide by 12 and so on. Also multiply `n` by 4 - the same number as you divided `r/100` by.

We do not know `A` and we do not know `P` but as we are doubling our money we can express `A` in terms of `P. A=2P`

`therefore 2P=P(1+(6/100)/4)^(4n)` 

`therefore (2P)/P=(1+0.06/4)^(4n)`

Now simplify

`therefore 2 = (1.015)^(4n)`

Use logs :

`log2= log 1.015^(4n)`

Simplify using the laws of logs :

`log2 = 4n log1.015`

`thereforelog2/log1.015 = 4n`

46.5555=  4n

46.5555 / 4 = n

n= 11.639 years

`therefore`your money will double in 12 years (to the nearest year).

Sources:
rhimshot415's profile pic

rhimshot415 | Middle School Teacher | eNotes Newbie

Posted on

Or you could just use the "Rule of 72" which says that to find out how long it would take to double your money divide 72 by the interest rate.

Therefore 2P=72/6 (6%) 

               2P=12 years.

The formula used by durbanville is mathematically correct, but I learned to use the "Rule of 72" when I was teaching a business math course.

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