Directions:  Use the Simple and Compound Interest equations for the following problems.
Show your work!

SIMPLE INTEREST				COMPOUND INTEREST

A = Future Value Amount		P = Principal Amount		r = Interest Rate (as decimal)
t = Time (in years)			n = Number of times interest is compounded per year

6.  You deposit $3,000 at 4% simple interest.  How much would you have in 10 years?

7.  You deposit $4,000 at 3% simple interest.  How much would you have in 20 years?

8.  You instead deposit the $4,000 in an account that pays 5% interest, compounded annually.

8(a).  How much would your account be worth in 20 years? $____________

8(b).  How much did you earn in interest? $____________

9.  You deposit $5,000 in an account that earns 6% interest, compounded monthly.

9(a).  How much would your account be worth in 10 years? $____________

9(b).  How much did you earn in interest? $____________

10.  You deposit $20,000 in an account that earns 8% interest, compounded quarterly.

10(a).  How much would your account be worth in 25 years? $____________

10(b).  How much did you earn in interest? $____________

To solve these problems, we'll use the formulas for simple and compound interest.

### 1. Simple Interest Formula:
\[ A = P(1 + rt) \]

Where:
- $ A $ = future value
- $ P $ = principal amount
- $ r $ = interest rate (as a decimal)
- $ t $ = time (in years)

### 2. Compound Interest Formula:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]

Where:
- $ A $ = future value
- $ P $ = principal amount
- $ r $ = interest rate (as a decimal)
- $ n $ = number of times interest is compounded per year
- $ t $ = time (in years)

Let's solve each of the problems step-by-step.

### Problem 6:
**You deposit $3,000 at 4% simple interest. How much would you have in 10 years?**

Given:
- $ P = 3000 $
- $ r = 0.04 $ (4%)
- $ t = 10 $

Using the simple interest formula:

\[
A = P(1 + rt) = 3000 \times (1 + 0.04 \times 10)
\]

\[
A = 3000 \times (1 + 0.4) = 3000 \times 1.4 = 4200
\]

**Answer: You would have $4,200 in 10 years.**

### Problem 7:
**You deposit $4,000 at 3% simple interest. How much would you have in 20 years?**

Given:
- $ P = 4000 $
- $ r = 0.03 $ (3%)
- $ t = 20 $

Using the simple interest formula:

\[
A = P(1 + rt) = 4000 \times (1 + 0.03 \times 20)
\]

\[
A = 4000 \times (1 + 0.6) = 4000 \times 1.6 = 6400
\]

**Answer: You would have $6,400 in 20 years.**

### Problem 8:
**You deposit $4,000 in an account that pays 5% interest, compounded annually.**

8(a). **How much would your account be worth in 20 years?**

Given:
- $ P = 4000 $
- $ r = 0.05 $ (5%)
- $ n = 1 $ (compounded annually)
- $ t = 20 $

Using the compound interest formula:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt} = 4000 \left(1 + \frac{0.05}{1}\right)^{1 \times 20}
\]

\[
A = 4000 \left(1.05\right)^{20}
\]

Let's calculate this value.

**8(a).** Your account would be worth approximately **$10,613.19** in 20 years.

8(b). **How much did you earn in interest?**

To find the interest earned:

\[
\text{Interest Earned} = A - P = 10613.19 - 4000 = 6613.19
\]

**Answer:** You earned approximately **$6,613.19** in interest.

### Problem 9:
**You deposit $5,000 in an account that earns 6% interest, compounded monthly.**

9(a). **How much would your account be worth in 10 years?**

Given:
- $ P = 5000 $
- $ r = 0.06 $ (6%)
- $ n = 12 $ (compounded monthly)
- $ t = 10 $

Using the compound interest formula:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt} = 5000 \left(1 + \frac{0.06}{12}\right)^{12 \times 10}
\]

Let's calculate this value.**9(a).** Your account would be worth approximately **$9,096.98** in 10 years.

9(b). **How much did you earn in interest?**

\[
\text{Interest Earned} = A - P = 9096.98 - 5000 = 4096.98
\]

**Answer:** You earned approximately **$4,096.98** in interest.

### Problem 10:
**You deposit $20,000 in an account that earns 8% interest, compounded quarterly.**

10(a). **How much would your account be worth in 25 years?**

Given:
- $ P = 20000 $
- $ r = 0.08 $ (8%)
- $ n = 4 $ (compounded quarterly)
- $ t = 25 $

Using the compound interest formula:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt} = 200

Learn how to calculate future values using simple and compound interest formulas. Solve problems like 'You deposit $3,000 at 4% simple interest. How much would you have in 10 years?' with step-by-step solutions.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation