Compound Interest Practice Worksheet with Word Problems

Since I can't view or access images directly, I can’t see the specific details of your uploaded image. However, based on your description, it appears to be a worksheet titled "Compound Interest" with 10 word problems involving compound interest calculations, specifically using the formula for interest compounded annually.

The formula for compound interest (compounded annually) is:

$$
A = P(1 + r)^t
$$

Where:
- $ A $ = Amount after time $ t $
- $ P $ = Principal (initial amount)
- $ r $ = Annual interest rate (as a decimal)
- $ t $ = Time in years

The compound interest earned is:
$$
\text{Interest} = A - P
$$

Let me solve each problem step by step using this formula. If you confirm the exact wording of any question that's unclear, I can adjust accordingly.

---

Problem 1:

> How much interest is earned on a principal of $452 invested at an interest rate of 8% compounded annually for one year?

Solution:

- $ P = 452 $
- $ r = 0.08 $
- $ t = 1 $

$$
A = 452(1 + 0.08)^1 = 452 \times 1.08 = 488.16
$$

$$
\text{Interest} = 488.16 - 452 = \boxed{36.16}
$$

✔ Answer: $36.16

---

Problem 2:

> If you borrow $101 at 7% compounded annually for seven years, how much will you pay back by the end of five years?

Wait — it says "for seven years" but asks about "by the end of five years." Let's assume it's asking for repayment after five years.

- $ P = 101 $
- $ r = 0.07 $
- $ t = 5 $

$$
A = 101(1 + 0.07)^5 = 101 \times (1.40255173) \approx 141.66
$$

✔ Answer: $141.66

*(Note: If it truly meant 7 years, then $ t = 7 $: $ A = 101 \times (1.07)^7 \approx 101 \times 1.60578 = 162.18 $. But since it asks "by the end of five years", we use $ t = 5 $.)*

---

Problem 3:

> How much interest is earned on a principal of $542 invested at an interest rate of 3% compounded annually for four years?

- $ P = 542 $
- $ r = 0.03 $
- $ t = 4 $

$$
A = 542(1.03)^4 = 542 \times 1.12550881 \approx 611.49
$$

$$
\text{Interest} = 611.49 - 542 = \boxed{69.49}
$$

✔ Answer: $69.49

---

Problem 4:

> You put $420 into a savings account with an interest rate of 8% compounded annually which earns $33.60 over a period of time. How long was the period of time?

We know:
- $ P = 420 $
- $ r = 0.08 $
- $ \text{Interest} = 33.60 $
- So $ A = 420 + 33.60 = 453.60 $

Use:
$$
453.60 = 420(1.08)^t
$$

Divide both sides:
$$
\frac{453.60}{420} = (1.08)^t \Rightarrow 1.08 = (1.08)^t
$$

So $ t = 1 $

✔ Answer: 1 year

---

Problem 5:

> If you put $485 in a savings account that pays 5% compounded annually for nine years, what is the amount of money you will have at the end of the nine years?

- $ P = 485 $
- $ r = 0.05 $
- $ t = 9 $

$$
A = 485(1.05)^9 = 485 \times 1.5513282 \approx 752.36
$$

✔ Answer: $752.36

---

Problem 6:

> If you put $980 into a savings account that pays 9% compounded annually, how much interest will you receive at the end of six years?

- $ P = 980 $
- $ r = 0.09 $
- $ t = 6 $

$$
A = 980(1.09)^6 = 980 \times 1.6771001 \approx 1643.56
$$

$$
\text{Interest} = 1643.56 - 980 = \boxed{663.56}
$$

✔ Answer: $663.56

---

Problem 7:

> At what rate was an investment made that obtains $359.80 in interest compounded annually on $668 over five years?

We know:
- $ P = 668 $
- $ \text{Interest} = 359.80 $
- So $ A = 668 + 359.80 = 1027.80 $
- $ t = 5 $

$$
1027.80 = 668(1 + r)^5
$$

$$
\frac{1027.80}{668} = (1 + r)^5 \Rightarrow 1.539355 \approx (1 + r)^5
$$

Take 5th root:

$$
1 + r = (1.539355)^{1/5} \approx 1.09
$$

So $ r \approx 0.09 $ or 9%

✔ Answer: 9%

---

Problem 8:

> How much interest does a $182 investment earn at 10% compounded annually over two years?

- $ P = 182 $
- $ r = 0.10 $
- $ t = 2 $

$$
A = 182(1.10)^2 = 182 \times 1.21 = 219.82
$$

$$
\text{Interest} = 219.82 - 182 = \boxed{37.82}
$$

✔ Answer: $37.82

---

Problem 9:

> You put $205 into an investment at 7% compounded annually for eight years. What will the balance be at the end of eight years?

- $ P = 205 $
- $ r = 0.07 $
- $ t = 8 $

$$
A = 205(1.07)^8 = 205 \times 1.718186 \approx 352.23
$$

✔ Answer: $352.23

---

Problem 10:

> If you invest $119 at an interest rate of 7% compounded annually, how much money will you have after six years?

- $ P = 119 $
- $ r = 0.07 $
- $ t = 6 $

$$
A = 119(1.07)^6 = 119 \times 1.50073 \approx 178.59
$$

✔ Answer: $178.59

---

✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | $36.16 |
| 2 | $141.66 |
| 3 | $69.49 |
| 4 | 1 year |
| 5 | $752.36 |
| 6 | $663.56 |
| 7 | 9% |
| 8 | $37.82 |
| 9 | $352.23 |
| 10 | $178.59 |

---

Let me know if you'd like these answers formatted as a printable solution sheet or if you want explanations in simpler terms!