Future value investment

Poseidon deposited 2,747 golden drachmas in a Mount Olympus college savings account to ensure Percy could attend college. It pays 0.04 (percent in decimal form) annual interest. After 11 years, he withdraws the money. How much more money would he have if the claim was continuously compounded versus compounded quarterly?

Correct answer:

x =  -27.0951

Step-by-step explanation:

$$\begin{gathered} a=2747 \\ t=11 \\ {n}_1=t=11 \\ {n}_2=t\cdot 4=11\cdot 4=44 \\ r=0.04 \\ {x}_1=a\cdot (1+r{)}^{n_1}=2747\cdot (1+0.04{)}^{11}\doteq 4228.8803 \\ {x}_2=a\cdot (1+r/4{)}^{n_2}=2747\cdot (1+0.04/4{)}^{44}\doteq 4255.9754 \\ x=x_1-x_2=4228.8803-4255.9754=-27.0951 \end{gathered}$$

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