Chapter 7.7, Problem 6STP

Suppose you deposit $2000 into an account earning $5\%$ interest compounded quarterly. To the nearest dollar, what is the balance after 4 years?

To determine

To determine the value of investment after 4 years.

Answer to Problem 6STP

The value after 4 years shall be approximately $2440.

Explanation of Solution

Given information:

Total amount invested is $2000 at 5% interest compounded quarterly.

We know that the amount P invested for time t at rate of r is given by,

  $A=P{\left(1+rn\right)}^{tn}$

(Here n is the number of times the amount is compounded)

Hence put the values given in the question we get,

(5% = 0.05)

  $\begin{array}{l}P=2000{\left(1+\frac{0.05}{4}\right)}^{4\times 4}\\ P=2000{\left(1+0.0125\right)}^{16}\\ P=2439.78\end{array}$

Hence the value after 4 years shall be approximately $2440.