Compound Interest - Word Problems worksheet with five real-life financial math problems.

Let's solve each of these compound interest word problems step by step using the compound interest formula:

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

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

---

Problem 1:

Frank deposited $3,400 into a savings account that pays 2% interest compounded monthly. How much money will he get after 8 years?

- $ P = 3400 $
- $ r = 0.02 $
- $ n = 12 $ (monthly)
- $ t = 8 $

$$
A = 3400 \left(1 + \frac{0.02}{12}\right)^{12 \times 8}
= 3400 \left(1 + 0.001666...\right)^{96}
= 3400 (1.001666...)^{96}
$$

Now calculate:

$$
(1.001666...)^{96} \approx 1.1735
$$

$$
A \approx 3400 \times 1.1735 = 3989.90
$$

✔ Answer: $3,989.90

---

Problem 2:

Vivien invests $7,500 in bonds at 3% interest compounded annually for 4 years.

- $ P = 7500 $
- $ r = 0.03 $
- $ n = 1 $ (annually)
- $ t = 4 $

$$
A = 7500 \left(1 + \frac{0.03}{1}\right)^{1 \times 4}
= 7500 (1.03)^4
$$

$$
(1.03)^4 = 1.12550881
$$

$$
A = 7500 \times 1.12550881 \approx 8441.32
$$

✔ Answer: $8,441.32

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Problem 3:

Anya deposits $4,550 at 3% interest compounded half-yearly for 6 years.

- $ P = 4550 $
- $ r = 0.03 $
- $ n = 2 $ (half-yearly)
- $ t = 6 $

$$
A = 4550 \left(1 + \frac{0.03}{2}\right)^{2 \times 6}
= 4550 (1 + 0.015)^{12}
= 4550 (1.015)^{12}
$$

$$
(1.015)^{12} \approx 1.195618
$$

$$
A = 4550 \times 1.195618 \approx 5440.62
$$

✔ Answer: $5,440.62

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Problem 4:

Mr. Turner invests $20,000 at 8% compounded half-yearly for 7 years.

- $ P = 20000 $
- $ r = 0.08 $
- $ n = 2 $
- $ t = 7 $

$$
A = 20000 \left(1 + \frac{0.08}{2}\right)^{2 \times 7}
= 20000 (1 + 0.04)^{14}
= 20000 (1.04)^{14}
$$

$$
(1.04)^{14} \approx 1.731676
$$

$$
A = 20000 \times 1.731676 \approx 34,633.52
$$

✔ Answer: $34,633.52

---

Problem 5:

Sharon deposits $520 at 6% interest compounded monthly for 1 year.

- $ P = 520 $
- $ r = 0.06 $
- $ n = 12 $
- $ t = 1 $

$$
A = 520 \left(1 + \frac{0.06}{12}\right)^{12 \times 1}
= 520 (1 + 0.005)^{12}
= 520 (1.005)^{12}
$$

$$
(1.005)^{12} \approx 1.061678
$$

$$
A = 520 \times 1.061678 \approx 552.07
$$

✔ Answer: $552.07

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✔ Final Answers:

1) $3,989.90
2) $8,441.32
3) $5,440.62
4) $34,633.52
5) $552.07

Let me know if you'd like the calculations shown with more decimal precision or steps!