Question

Suppose that $2000 is placed in an account that pays 12% interest compounded each year.Assume that no withdrawals are made from the account.Follow the instructions below. Do not do any rounding.

Answer 1

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:

$A=P(1+\frac{r}{n})^{nt}$

(a)

Amount after 1 year is:

$\begin{gathered} t=1 \\ \\ r=\frac{12}{100} \\ \\ r=0.12 \\ \\ n=1 \\ \\ P=2000 \end{gathered}$

So the amount is:

$\begin{gathered} A=2000(1+\frac{0.12}{1})^{1\times1} \\ \\ A=2000(1.12) \\ \\ A=2240 \end{gathered}$

After one year amount in the account is $2240

(b)

Amount after two years is:

$\begin{gathered} t=2 \\ \\ n=1 \\ \\ r=0.12 \\ \\ P=2000 \end{gathered}$

So amount is:

$\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \\ A=2000(1+\frac{0.12}{1})^{1\times2} \\ \\ A=2000(1.12)^2 \\ \\ A=2000\times1.2544 \\ \\ A=2508.8 \end{gathered}$

After two years amount in the account is $2508.8