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+(r)/(n))^(nt)`

(a)

Amount after 1 year is:

`\begin{gathered} t=1 \\ \\ r=(12)/(100) \\ \\ r=0.12 \\ \\ n=1 \\ \\ P=2000 \end{gathered}`

So the amount is:

`\begin{gathered} A=2000(1+(0.12)/(1))^(1*1) \\ \\ 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+(r)/(n))^(nt) \\ \\ A=2000(1+(0.12)/(1))^(1*2) \\ \\ A=2000(1.12)^2 \\ \\ A=2000*1.2544 \\ \\ A=2508.8 \end{gathered}`

After two years amount in the account is $2508.8