Printable math worksheet titled "Compound Interest - Word Problems" with five word problems related to calculating compound interest in different financial situations.

To solve these compound interest problems, we will use the compound interest formula:

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

Where:
- \( A \) is the amount of money accumulated after \( t \) years, including interest.
- \( P \) is the principal amount (initial deposit).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of times interest is compounded per year.
- \( t \) is the time the money is invested for in years.

Let's solve each problem step by step.

---

Problem 1:

Frank deposited \$3,400 into a savings account that pays 2% in interest compounded monthly. How much money will he get after 8 years? Round your answer to the nearest cent.

#### Given:
- \( P = 3400 \)
- \( r = 2\% = 0.02 \)
- \( n = 12 \) (compounded monthly)
- \( t = 8 \)

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

#### Substituting the values:
\[
A = 3400 \left(1 + \frac{0.02}{12}\right)^{12 \times 8}
\]
\[
A = 3400 \left(1 + 0.001667\right)^{96}
\]
\[
A = 3400 \left(1.001667\right)^{96}
\]

#### Calculate \( (1.001667)^{96} \):
Using a calculator:
\[
(1.001667)^{96} \approx 1.179085
\]

#### Now calculate \( A \):
\[
A = 3400 \times 1.179085 \approx 4008.89
\]

#### Final Answer:
\[
\boxed{4008.89}
\]

---

Problem 2:

Vivien is saving money so she can open a coffee shop after 4 years. She invests \$7,500 in bonds, and the interest rate is 3% compounded annually. How much money will Vivien have when it's time to open the shop?

#### Given:
- \( P = 7500 \)
- \( r = 3\% = 0.03 \)
- \( n = 1 \) (compounded annually)
- \( t = 4 \)

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

#### Substituting the values:
\[
A = 7500 \left(1 + \frac{0.03}{1}\right)^{1 \times 4}
\]
\[
A = 7500 \left(1 + 0.03\right)^4
\]
\[
A = 7500 \left(1.03\right)^4
\]

#### Calculate \( (1.03)^4 \):
Using a calculator:
\[
(1.03)^4 \approx 1.125509
\]

#### Now calculate \( A \):
\[
A = 7500 \times 1.125509 \approx 8441.32
\]

#### Final Answer:
\[
\boxed{8441.32}
\]

---

Problem 3:

Anya deposits \$4,550 in an account that offers 3% in interest compounded half-yearly. She is planning to fund her child's higher studies with this money. How much money, rounded to the nearest cent, will be in the account after 6 years?

#### Given:
- \( P = 4550 \)
- \( r = 3\% = 0.03 \)
- \( n = 2 \) (compounded half-yearly)
- \( t = 6 \)

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

#### Substituting the values:
\[
A = 4550 \left(1 + \frac{0.03}{2}\right)^{2 \times 6}
\]
\[
A = 4550 \left(1 + 0.015\right)^{12}
\]
\[
A = 4550 \left(1.015\right)^{12}
\]

#### Calculate \( (1.015)^{12} \):
Using a calculator:
\[
(1.015)^{12} \approx 1.201947
\]

#### Now calculate \( A \):
\[
A = 4550 \times 1.201947 \approx 5470.28
\]

#### Final Answer:
\[
\boxed{5470.28}
\]

---

Problem 4:

Mr. Turner invests \$20,000 in a retirement account. The investment is for 7 years, and the interest rate is 8% compounded half-yearly. What will be the final balance rounded to the nearest cent?

#### Given:
- \( P = 20000 \)
- \( r = 8\% = 0.08 \)
- \( n = 2 \) (compounded half-yearly)
- \( t = 7 \)

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

#### Substituting the values:
\[
A = 20000 \left(1 + \frac{0.08}{2}\right)^{2 \times 7}
\]
\[
A = 20000 \left(1 + 0.04\right)^{14}
\]
\[
A = 20000 \left(1.04\right)^{14}
\]

#### Calculate \( (1.04)^{14} \):
Using a calculator:
\[
(1.04)^{14} \approx 1.741101
\]

#### Now calculate \( A \):
\[
A = 20000 \times 1.741101 \approx 34822.02
\]

#### Final Answer:
\[
\boxed{34822.02}
\]

---

Problem 5:

Sharon deposited \$520 in a new regular savings account that earns 6% in interest compounded monthly. How much will she get at the end of the year?

#### Given:
- \( P = 520 \)
- \( r = 6\% = 0.06 \)
- \( n = 12 \) (compounded monthly)
- \( t = 1 \)

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

#### Substituting the values:
\[
A = 520 \left(1 + \frac{0.06}{12}\right)^{12 \times 1}
\]
\[
A = 520 \left(1 + 0.005\right)^{12}
\]
\[
A = 520 \left(1.005\right)^{12}
\]

#### Calculate \( (1.005)^{12} \):
Using a calculator:
\[
(1.005)^{12} \approx 1.061678
\]

#### Now calculate \( A \):
\[
A = 520 \times 1.061678 \approx 552.07
\]

#### Final Answer:
\[
\boxed{552.07}
\]

---

Final Answers:

1. \(\boxed{4008.89}\)
2. \(\boxed{8441.32}\)
3. \(\boxed{5470.28}\)
4. \(\boxed{34822.02}\)
5. \(\boxed{552.07}\)