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? 

Expert Answers

An illustration of the letter 'A' in a speech bubbles

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).

Approved by eNotes Editorial Team