Question

Suppose that $2000 is placed in an account that pays 7% interest compounded each year.Assume that no withdrawals are made from the account.Follow the instructions below. Do not do any rounding.(a) Find the amount in the account at the end of 1 year.(b) Find the amount in the account at the end of 2 years.siX?

Answer 1

We are given

Principal (P) = $2000

Rate (r) = 7% = 0.07

We want to find the amount at the end of 1 year and 2 years compound interest

Solution

Recall the formula for the compound interest

`A=P(1+(r)/(n))^(nt)`

Here

`\begin{gathered} A\text{ = amount} \\ n\text{ = }numberoftimesinterestappliedpertimeperiod \\ t\text{ = time} \end{gathered}`

other parameters have been defined earlier above

Part A

Find the amount in the account at the end of 1 year.

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ A=2000(1+(0.07)/(1))^((1)(1)) \\ \text{Notice that n = 1 and t = 1 year} \\ A=2000(1+0.07)^1 \\ A=2000(1.07) \\ A=2140 \end{gathered}`

Therefore amount = $2140

Part B

Find the amount in the account at the end of 2 years.

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ \\ A=2000(1+(0.07)/(1))^((1)(2)) \\ \text{Notice that n = 1 and t = 2 years} \\ A=2000(1+0.07)^2 \\ A=2000(1.07)^2 \\ A=2000(1.1449) \\ A=2289.8 \end{gathered}`

Therefore, the amount = $2289.8