Answer:
He have to deposit $520.49 as Principal to have enough money in 3 years to buy the bike.
[tex]\text{ \$520.49}[/tex]Explanation:
The formula for calculating the Future value of Compound interest is;
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where;
A = Future Value/Amount
P = Principal
r = Interest rate (decimal)
n = number of times the interest is compounded per unit time "t"
t = Time
Making the Principal P the subject of formula;
[tex]P=\frac{A}{(1+\frac{r}{n})^{nt}}[/tex]Given;
A = $700.00
r = 10% = 0.10
n = compounded quarterly (4 times a year) = 4
t = 3 years
substituting the given values;
[tex]\begin{gathered} P=\frac{\text{ \$700.00}}{(1+\frac{0.10}{4})^{4(3)}}=\frac{\text{ \$700.00}}{(1.025)^{12}} \\ P=\text{ \$520.49} \end{gathered}[/tex]Therefore, he have to deposit $520.49 as Principal to have enough money in 3 years to buy the bike.
[tex]\text{ \$520.49}[/tex]