superannuation

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?

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

When a bank says that the interest rate is 4.5% with interest compounded monthly, that means that after each month your investiment $I$ grows by $\frac{4.5\%}{12}$ (=4.5/1200 or 0.045/12), so that it becomes $I_1 = I+\frac{0.045}{12}I=I\left(1+\frac{0.045}{12}\righ t)$ . After another month, the interest is computed from what you now have (i.e. $I_1$ ), thus after two months you have $I_2=I_1+\frac{0.045}{12}I_1=I\left(1+\frac{0.045}{ 12}\right)^2$ and so on, after $n$ month you have $I_n=I \left(1+\frac{0.045}{12}\right)^n$ .

Note that after one year you have $\left(1+\frac{0.045}{12}\right)^{12}\simeq 1.0459$ , thus the annual rate is a bit more than 4.5%. If I were a bankier, I would define the monthly rate to be $\left(1+0.045\right)^{1/12}-1$ , it would make more sense! (especially if I am the bankier)