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

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

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.

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

Therefore amount = $2140

Part B

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

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

Therefore, the amount = $2289.8