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
---
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
---
Problem 4:
Mr. Turner invests $20,000 at 8% interest 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
---
✔ Final Answers:
1)
$3,989.90
2)
$8,441.32
3)
$5,440.62
4)
$34,633.52
5)
$552.07
All rounded to the nearest cent.
Let me know if you'd like these steps explained in simpler terms or with a calculator method!
Parent Tip: Review the logic above to help your child master the concept of compound interest word problems worksheet.
