Questions: The principal P is borrowed at a simple interest rate r for a period of time t. Find the loan's future value A, or the total amount due at time t. P= 7000, r=6 %, t=6 years (Round to the nearest cent as needed.)

The principal P is borrowed at a simple interest rate r for a period of time t. Find the loan's future value A, or the total amount due at time t. P= 7000, r=6 %, t=6 years (Round to the nearest cent as needed.)
Transcript text: This quiz: 10 point(s) possible This question: 1 point(s) possible Submit quiz The principal $P$ is borrowed at a simple interest rate r for a period of time t . Find the loan's future value A , or the total amount due at time $t$. \[ P=\$ 7000, r=6 \%, t=6 \text { years } \] \$ $\square$ (Round to the nearest cent as needed.)
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Solution

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Solution Steps

Step 1: Convert the Annual Interest Rate to a Decimal

To convert the annual interest rate from a percentage to a decimal, we divide it by 100. Thus, \(r = 6 / 100 = 0.06\).

Step 2: Calculate the Future Value

Using the formula \(A = P(1 + rt)\), where \(P = 7000\), \(r = 0.06\), and \(t = 6\), we calculate the future value. Substitute the values into the formula: \(A = 7000(1 + 0.06 \times 6)\).

Final Answer:

The future value \(A\) after 6 years at an annual interest rate of 6% is approximately 9520.

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