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Introduction to compound interost

Suppose Carmen borrows at an Interest rate of compounded each year. Assume that no payments are made on the loan.

Follow the instructions below. Do not do any rounding.
(a) Find the amount owed at the end of 1 year.

(b) Find the amount owed at the end of 2 years.

Ask by Boyd Haynes. in the United States

Mar 29,2025

Question

Capital SD Links
Demographic
Spotify - Search
A Growing Econom…
Clower I Lod
Linear Equalions
Introduction to compound interost

Suppose Carmen borrows at an Interest rate of compounded each year. Assume that no payments are made on the loan.

Follow the instructions below. Do not do any rounding.
(a) Find the amount owed at the end of 1 year.

(b) Find the amount owed at the end of 2 years.

Ask by Boyd Haynes. in the United States

Mar 29,2025

UpStudy AI · Accepted Answer

**Step 1: Write the compound interest formula**

The compound interest formula is  
$$
A = P(1+r)^n
$$  
where  
$$P$$ is the principal (initial amount),  
$$r$$ is the annual interest rate (in decimal), and  
$$n$$ is the number of years.

---

**Step 2: Identify the given values**

Here,  
$$P = 7000$$,  
$$r = 0.02$$ (since $$2\% = 0.02$$),  
and $$n$$ will be the number of years for each part.

---

**(a) Find the amount owed at the end of 1 year**

For $$n=1$$, substitute the values into the formula:  
$$
A = 7000(1+0.02)^1 = 7000(1.02)
$$

Multiply:  
$$
7000 \times 1.02 = 7140
$$

Thus, the amount owed at the end of 1 year is  
$$
\$7140
$$

---

**(b) Find the amount owed at the end of 2 years**

For $$n=2$$, substitute the values into the formula:  
$$
A = 7000(1+0.02)^2 = 7000(1.02)^2
$$

First, calculate $$(1.02)^2$$:  
$$
(1.02)^2 = 1.0404
$$

Then multiply:  
$$
7000 \times 1.0404 = 7282.8
$$

Thus, the amount owed at the end of 2 years is  
$$
\$7282.8
$$
**(a) Amount owed at the end of 1 year: \$7140** **(b) Amount owed at the end of 2 years: \$7282.80**

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