The compound interest formula is given by:
[tex]I=P(1+\frac{r}{n})^{tn}[/tex]where,
P: principal investment = $400
r: interest rate = 3% = 0.03
n: times at year = 4 quarterly
t: years = 0, 5 , 10, 15, 20
Replace the previous values of the parameters into the formula for I and simplify for each value of t:
[tex]\begin{gathered} I_0=400(1+\frac{0.03}{4})^{0\cdot4}=400(1+0.0075)^0=400(1.0075)^0=400 \\ I_5=400(1.0075)^{5\cdot4}\approx464.5 \\ I_{10}=400(1.0075)^{10\cdot4}\approx539.3 \\ I_{15}=400(1.0075)^{15\cdot4}\approx626.3 \\ I_{20}=400(1.0075)^{20\cdot4}\approx727.2 \end{gathered}[/tex]Hence, the amounts for t=0, 5, 10, 15 and 20 years are, respectivelly:
$400
$464.5
$539.3
$626.3
$727.2
