# superannuation

An amount of $1500 is invested at a rate of 4.5% per annum with the interest compounded monthly. How long will it take for the investment to double its value? Im unclear as to why they use this formula : 1500 (1+4.5/1200)^t = 3000 If someone could explain this to me, it would be greatly appreciated, thank you • Jan 14th 2010, 04:25 AM Laurent Quote: Originally Posted by christina An amount of$1500 is invested at a rate of 4.5% per annum with the interest compounded monthly. How long will it take for the investment to double its value?
When a bank says that the interest rate is 4.5% with interest compounded monthly, that means that after each month your investiment $\displaystyle I$ grows by $\displaystyle \frac{4.5\%}{12}$ (=4.5/1200 or 0.045/12), so that it becomes $\displaystyle I_1 = I+\frac{0.045}{12}I=I\left(1+\frac{0.045}{12}\righ t)$. After another month, the interest is computed from what you now have (i.e. $\displaystyle I_1$), thus after two months you have $\displaystyle I_2=I_1+\frac{0.045}{12}I_1=I\left(1+\frac{0.045}{ 12}\right)^2$ and so on, after $\displaystyle n$ month you have $\displaystyle I_n=I \left(1+\frac{0.045}{12}\right)^n$.
Note that after one year you have $\displaystyle \left(1+\frac{0.045}{12}\right)^{12}\simeq 1.0459$, thus the annual rate is a bit more than 4.5%. If I were a bankier, I would define the monthly rate to be $\displaystyle \left(1+0.045\right)^{1/12}-1$, it would make more sense! (especially if I am the bankier)