Chapter 4.1, Problem 37PS

Solution

a.

To find: The balance in the account after 4 years.

The balance in the account after 4 years is $2479.38.

Given:

The deposited amount is $2200 in the account paying 3% annual interest compounded quarterly.

Concept used:

The amount $A$ in the account after $t$ years is given by,

  $A=P{\left(1+\frac{r}{n}\right)}^{nt}$ , where $P$ is the initial principal deposited in an account paying an annual interest rate $r$ (expressed as a decimal), compounded $n$ times per year.

Calculation:

Here,

  $P=\$2200,r=0.03,n=4,t=4$ .

Now, the amount in the account after 4 years is

  $\begin{array}{c}A=2200{\left(1+\frac{0.03}{4}\right)}^{4\times 4}\\ =2200{\left(1.0075\right)}^{16}\\ \approx 2479.38\end{array}$

Hence, the balance in the account after 4 years is $2479.38.

b.

To find: The balance in the account after 4 years.

The balance in the account after 4 years is $2406.98.

Given:

The deposited amount is $2200 in the account paying 2.25% annual interest compounded monthly.

Concept used:

The amount $A$ in the account after $t$ years is given by,

  $A=P{\left(1+\frac{r}{n}\right)}^{nt}$ , where $P$ is the initial principal deposited in an account paying an annual interest rate $r$ (expressed as a decimal), compounded $n$ times per year.

Calculation:

Here,

  $P=\$2200,r=0.0225,n=12,t=4$ .

Now, the amount in the account after 4 years is

  $\begin{array}{c}A=2200{\left(1+\frac{0.0225}{12}\right)}^{12\times 4}\\ =2200{\left(1.001875\right)}^{48}\\ \approx 2406.98\end{array}$

Hence, the balance in the account after 4 years is $2406.98.

c.

To find: The balance in the account after 4 years.

The balance in the account after 4 years is $2383.23.

Given:

The deposited amount is $2200 in the account paying 2% annual interest compounded daily.

Concept used:

The amount $A$ in the account after $t$ years is given by,

  $A=P{\left(1+\frac{r}{n}\right)}^{nt}$ , where $P$ is the initial principal deposited in an account paying an annual interest rate $r$ (expressed as a decimal), compounded $n$ times per year.

Calculation:

Here,

  $P=\$2200,r=0.02,n=365,t=4$ .

Now, the amount in the account after 4 years is

  $\begin{array}{c}A=2200{\left(1+\frac{0.02}{365}\right)}^{365\times 4}\\ =2200{\left(1.0000547945\right)}^{1460}\\ \approx 2383.23\end{array}$

Hence, the balance in the account after 4 years is $2383.23.