Chapter 0.3, Problem 8QR

To determine

To find: To find the value of investing $P$ dollars for $n$ years with the interest rate $r$ compounded annually.

Answer to Problem 8QR

  $\$1019.02$ approximately.

Explanation of Solution

Given information: Find the value of investing $P$ dollars for $n$ years with the interest rate $r$ compounded annually.

  $P=\$1000,r=6.3\%,n=3\text{years}$

Concept used: If an account starts with principal $P$ and earns an annual interest rate $r$ compounded annually, then the value of the account in $n$ years will be:

  $A=P{\left(1+r\right)}^n$

Calculation:

The compound interest is compounded annually at the rate of $6.3\%$:

Convert rate percent into decimal:

  $r=6.3\%=\frac{6.3}{100}=0.063$

Since the interest is compounded annually, use the following formula to calculate the amount:

  $A=P{\left(1+r\right)}^n$

Substitute $P=1000$ , $r=0.063$ and $n=3$ in the above formula:

  $\begin{array}{l}A=1000{\left(1+0.063\right)}^3\\ =1000{\left(1.0063\right)}^3\\ \approx 1019.02\end{array}$

Therefore, the amount will be $\$1019.02$ approximately.