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=​$40004000​, 

requals=3.53.5​%, 

tequals=99 

months

Question content area bottom

Part 1

The future value is 

​$enter your response here. 

​(Simplify your answer. Type an integer or a​ decimal.)

To find the future value $ A $ of a loan with simple interest, we can use the formula:

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

Where:
- $ P $ is the principal (initial amount),
- $ r $ is the interest rate per period,
- $ t $ is the time the loan is held.

Given:
- $ P = 4000 $,
- $ r = 3.5\% = 0.035 $ (as a decimal),
- $ t = 9 $ months.

First, convert the time from months to years, because the interest rate is typically annual:

\[
t = \frac{9}{12} = 0.75 \text{ years}.
\]

Now substitute the values into the formula:

\[
A = 4000 \times \left( 1 + 0.035 \times 0.75 \right).
\]

\[
A = 4000 \times (1 + 0.02625).
\]

\[
A = 4000 \times 1.02625 = 4105.
\]

So, the future value $ A $ is **$4105**.

Would you like more details or have any questions?  
Here are 5 related questions:

1. How would the future value change if the time period were doubled?
2. What is the total interest earned on this loan?
3. How does the simple interest formula differ from compound interest?
4. How would the future value change if the interest rate increased to 5%?
5. How does the principal amount affect the future value?

**Tip:** Always ensure that the interest rate and time period units match (e.g., both annual).

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 = $4000, r = 3.5%, t = 9 months.

Learn how to calculate the future value of a loan with simple interest. In this example, a principal of $4000 is borrowed at an interest rate of 3.5% for 9 months. This step-by-step guide will walk you through the formula and process to find the total amount due. Suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation