Given:
Principal amount = $2000
Interest rate = 12%
Find-:
(a) Amount in an account at the end of 1 year
(b)Amount in an account at the end of 2 year
Sol:
Compounded interest rate is:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex](a)
Amount after 1 year is:
[tex]\begin{gathered} t=1 \\ \\ r=\frac{12}{100} \\ \\ r=0.12 \\ \\ n=1 \\ \\ P=2000 \end{gathered}[/tex]So the amount is:
[tex]\begin{gathered} A=2000(1+\frac{0.12}{1})^{1\times1} \\ \\ A=2000(1.12) \\ \\ A=2240 \end{gathered}[/tex]After one year amount in the account is $2240
(b)
Amount after two years is:
[tex]\begin{gathered} t=2 \\ \\ n=1 \\ \\ r=0.12 \\ \\ P=2000 \end{gathered}[/tex]So amount is:
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \\ A=2000(1+\frac{0.12}{1})^{1\times2} \\ \\ A=2000(1.12)^2 \\ \\ A=2000\times1.2544 \\ \\ A=2508.8 \end{gathered}[/tex]After two years amount in the account is $2508.8