How Long to Double Your Money with Compound Interest?

[jahaddow]

A fixed deposit investment attracts interest of 4.3% p.a. compounded annually. How long will $30 000 take to double in value?

 

[Mark44]

A fixed deposit investment attracts interest of 4.3% p.a. compounded annually. How long will $30 000 take to double in value?

What have you tried? What are the relevant equations?

 

[jahaddow]

This is all I know, I don't know what method should be used to find the answer?

 

[HallsofIvy]

That's very peculiar! If you aren't taking a course that has discussed "compound interest", why have you been assigned a problem like this? If you are then surely there are formulas for compound interest in your textbook aren't there?

If I remember correctly, after n years, an amount S at r rate of interest (so that 100r% is the annual percentage rate) compounded annually is given by $S(1+ r)^n$. Set that equal to 2S, cancel the "S"s and solve for n.

 

[quantum13]

A powerful strategy is to think about the specific case and try to obtain a general equation.

The first year, you have $30 000

The second year it is compounded by $30 000 x .043 so you have 30 000 + 30 000 x .043
= 30 000 (1.043)

The next year your money increases again by 30 000 (1.043) (.043) for a total of 30 000 (1.043) + 30 000 (1.043) (.043) = 30 000 (1.043) (1.043) = 30 000 (1.043)^2

By now you should have noticed a pattern.