Question

Compounding - compare accounts: Ruby invested $850 in an account paying an interest rate of 2 % compoundedquarterly. Logan invested $850 in an account paying an interest rate of 2 %compounded monthly. After 17 years, how much more money would Ruby have inher account than Logan, to the nearest dollar?

Answer 1

First let's calculate the final value for Ruby's money:

$\begin{gathered} P=850 \\ i=0.02 \\ n=4 \\ t=17 \\ \Rightarrow A=850\cdot(1+\frac{0.02}{4})^{17\cdot4} \\ \Rightarrow A=850\cdot(1.005)^{68}=1193.19 \end{gathered}$

Now let's do the same for Logan's money:

$\begin{gathered} P=850 \\ i=0.02 \\ n=12 \\ t=17 \\ \Rightarrow A=850\cdot(1+\frac{0.02}{12})^{17\cdot12}=850(1.0016667)^{204} \\ A=1193.87 \end{gathered}$

As we can see, Ruby and Logan have almost the same amount of money after 17 years.