SOLUTION
To solve this we would use the formula
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ where\text{ } \\ A=amount\text{ after time t = 24,000 + 1200 = \$25,200} \\ P=money\text{ invested = \$24,000} \\ r=interest\text{ rate = ?} \\ t=time\text{ in years = 3.2 years } \\ n=number\text{ of compounding = 4} \end{gathered}[/tex]
Applying we have
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ 25,200=24,000(1+\frac{r}{4})^^{4\times3.2} \\ 25,200=24,000(1+\frac{r}{4})^{12.8} \\ (1+\frac{r}{4})^{12.8}=\frac{25200}{24000} \\ (1+\frac{r}{4})^{12.8}=1.05 \\ (\frac{4+r}{4})^{12.8}=1.05 \end{gathered}[/tex]
Continuing we have
[tex]\begin{gathered} \frac{4+r}{4}=(1.05)^{\frac{1}{12.8}} \\ \frac{4+r}{4}=1.003819 \\ 4+r=4\times1.003819 \\ r=4.0152760-4 \\ r=0.015276 \end{gathered}[/tex]
The rate becomes
[tex]\begin{gathered} r=0.015276\times100 \\ r=1.5276 \end{gathered}[/tex]
Hence r = 1.53%
