Given information:
Deposit amount = P = $100
Interest rate = r = 10% = 0.10
Compounding interval = n = quarterly = 4
Number of years = t = 2
Solution:
Recall that the compound interest formula is given by
[tex]A=P(1+\frac{r}{n})^{n\cdot t}[/tex]Where
A = Accumulated amount (or ending balance)
P = Principle amount (or deposit amount)
r = Interest rate in decimal
n = Number of compounding in a year
t = Number of years
Now let us substitute the given values into the above formula
[tex]\begin{gathered} A=100\cdot(1+\frac{0.10}{4})^{4\cdot2} \\ A=100\cdot(1+0.025)^8 \\ A=100\cdot(1.025)^8 \\ A=100\cdot(1.2184) \\ A=\$121.84 \end{gathered}[/tex]Therefore, Zack will be able to spend $121.84 on the bike.
