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).

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial