The principal P is borrowed at 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.
Pequals=​$26,000​, requals=6.5%, tequals=5 years

To calculate the future value $ A $ of a loan under simple interest, we use the formula:

\[
A = P(1 + rt)
\]

where:
- $ P $ is the principal (initial amount),
- $ r $ is the annual interest rate (in decimal form),
- $ t $ is the time in years.

### Given:
- $ P = 26,000 $ (the principal),
- $ r = 6.5\% = 0.065 $ (the interest rate as a decimal),
- $ t = 5 $ years.

Now, substitute these values into the formula:

\[
A = 26,000(1 + 0.065 \times 5)
\]
\[
A = 26,000(1 + 0.325)
\]
\[
A = 26,000(1.325)
\]
\[
A = 34,450
\]

So, the future value $ A $, or the total amount due after 5 years, is **$34,450**.

Would you like more details, or do you have any further questions?

Here are 5 related questions:
1. How would the total amount change if the interest rate increased to 7%?
2. What is the total interest earned on this loan after 5 years?
3. How does simple interest differ from compound interest in terms of future value?
4. If the loan were for 3 years instead of 5, what would be the future value?
5. How can we determine the time required for a loan to double at a given interest rate?

**Tip:** Always convert the interest rate to a decimal form before using it in formulas.

The principal P is borrowed at 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 = $26,000​, r = 6.5%, t = 5 years.

Learn how to calculate the future value of a loan using the simple interest formula A = P(1 + rt). In this example, with a principal of $26,000, an interest rate of 6.5%, and a time period of 5 years, the total amount due at the end of the period is $34,450. This detailed explanation is ideal for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation