Given:
Invest Amount = 13000
Time = 1 year
Compound daily = 10%
Compound continuously = 9.86%
Sol:
The compound interest formula is:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where,
[tex]\begin{gathered} A=\text{ Amount after ''n'' year.} \\ P=\text{ Principal amount } \\ r=\text{ Rate} \\ n=\text{ Number of time in compounded per year.} \\ t=\text{ Number of years} \end{gathered}[/tex][tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \\ A=13000(1+\frac{0.1}{365})^{365\times1} \\ \\ A=13000(1+2.74\times10^{-4})^{365} \\ \\ A=13000(1.000274)^{365} \\ \\ A=13000\times1.1052 \\ \\ A=14367.025 \\ \end{gathered}[/tex]So the amount is 14367.025
(b)
When compounded continuously.
[tex]\begin{gathered} A=P\times e^{rt} \\ \end{gathered}[/tex][tex]\begin{gathered} A=P\times e^{rt} \\ \\ A=13000\times e^{(0.0986\times1)} \\ \\ A=13000\times2.68 \\ \\ A=34846.38 \end{gathered}[/tex]So the amount is 34846.38
