Compound Interest Worksheets - Math About - Free Printable

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

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

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

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1.) You invested $52,400 at 6% compounded annually for 5 years. What is your total return?

- $ P = 52,400 $
- $ r = 0.06 $
- $ n = 1 $ (annually)
- $ t = 5 $

$$
A = 52,400 \left(1 + \frac{0.06}{1}\right)^{1 \times 5} = 52,400 (1.06)^5
$$

Calculate $ (1.06)^5 $:
$$
(1.06)^5 \approx 1.3382256
$$

$$
A \approx 52,400 \times 1.3382256 \approx 70,157.52
$$

✔ Answer: $70,157.52

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2.) You borrowed $10,400 for 4 years at 12.7% and the interest is compounded semi-annually. What is the total you will pay back?

- $ P = 10,400 $
- $ r = 0.127 $
- $ n = 2 $ (semi-annual)
- $ t = 4 $

$$
A = 10,400 \left(1 + \frac{0.127}{2}\right)^{2 \times 4} = 10,400 \left(1 + 0.0635\right)^8
= 10,400 (1.0635)^8
$$

Calculate $ (1.0635)^8 $:
$$
(1.0635)^8 \approx 1.6546
$$

$$
A \approx 10,400 \times 1.6546 \approx 17,207.84
$$

✔ Answer: $17,207.84

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3.) Your 2-year investment of $5,300 earns 2.9% and is compounded annually. What will your total return be?

- $ P = 5,300 $
- $ r = 0.029 $
- $ n = 1 $
- $ t = 2 $

$$
A = 5,300 (1 + 0.029)^2 = 5,300 (1.029)^2
$$

$ (1.029)^2 \approx 1.058841 $

$$
A \approx 5,300 \times 1.058841 \approx 5,611.86
$$

✔ Answer: $5,611.86

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4.) You invested $100 at 8.2% which is compounded annually for 7 years. How much will your $100 be worth in 7 years?

- $ P = 100 $
- $ r = 0.082 $
- $ n = 1 $
- $ t = 7 $

$$
A = 100 (1 + 0.082)^7 = 100 (1.082)^7
$$

$ (1.082)^7 \approx 1.7527 $

$$
A \approx 100 \times 1.7527 = 175.27
$$

✔ Answer: $175.27

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5.) Your investment of $18,100 at 13.6% compounded quarterly for 7½ years will be worth how much?

- $ P = 18,100 $
- $ r = 0.136 $
- $ n = 4 $ (quarterly)
- $ t = 7.5 $

$$
A = 18,100 \left(1 + \frac{0.136}{4}\right)^{4 \times 7.5} = 18,100 (1 + 0.034)^{30}
= 18,100 (1.034)^{30}
$$

$ (1.034)^{30} \approx 2.847 $

$$
A \approx 18,100 \times 2.847 \approx 51,480.70
$$

✔ Answer: $51,480.70

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6.) You invested your allowance of $270 which gets 15% compounded annually for 3 years. How much will you have in 3 years?

- $ P = 270 $
- $ r = 0.15 $
- $ n = 1 $
- $ t = 3 $

$$
A = 270 (1 + 0.15)^3 = 270 (1.15)^3
$$

$ (1.15)^3 = 1.520875 $

$$
A \approx 270 \times 1.520875 \approx 410.64
$$

✔ Answer: $410.64

---

7.) You gave your friend a short-term 2-year loan of $43,000 at 3% compounded annually. What was your total return?

- $ P = 43,000 $
- $ r = 0.03 $
- $ n = 1 $
- $ t = 2 $

$$
A = 43,000 (1 + 0.03)^2 = 43,000 (1.03)^2 = 43,000 \times 1.0609 = 45,618.70
$$

✔ Answer: $45,618.70

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8.) Your investment of $1,200 gets 5.1% and is compounded semi-annually for 7½ years. What will your $1,200 be worth at the end of the term?

- $ P = 1,200 $
- $ r = 0.051 $
- $ n = 2 $
- $ t = 7.5 $

$$
A = 1,200 \left(1 + \frac{0.051}{2}\right)^{2 \times 7.5} = 1,200 (1 + 0.0255)^{15}
= 1,200 (1.0255)^{15}
$$

$ (1.0255)^{15} \approx 1.4637 $

$$
A \approx 1,200 \times 1.4637 \approx 1,756.44
$$

✔ Answer: $1,756.44

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9.) You borrowed $95 for 1 year at 5.2% interest that is compounded semi-annually. What will you pay back in full?

- $ P = 95 $
- $ r = 0.052 $
- $ n = 2 $
- $ t = 1 $

$$
A = 95 \left(1 + \frac{0.052}{2}\right)^{2 \times 1} = 95 (1 + 0.026)^2 = 95 (1.026)^2
$$

$ (1.026)^2 = 1.052676 $

$$
A \approx 95 \times 1.052676 \approx 99.99
$$

✔ Answer: $99.99 (approximately)

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10.) Your 6 and 2/3 year investment of $1,450 at 5.4% compounded monthly brought you a grand total of?

- $ P = 1,450 $
- $ r = 0.054 $
- $ n = 12 $ (monthly)
- $ t = 6 + \frac{2}{3} = \frac{20}{3} \approx 6.6667 $ years

$$
A = 1,450 \left(1 + \frac{0.054}{12}\right)^{12 \times \frac{20}{3}} = 1,450 (1 + 0.0045)^{80}
= 1,450 (1.0045)^{80}
$$

$ (1.0045)^{80} \approx 1.4323 $

$$
A \approx 1,450 \times 1.4323 \approx 2,071.84
$$

✔ Answer: $2,071.84

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✔ Final Answers Summary:

1. $70,157.52
2. $17,207.84
3. $5,611.86
4. $175.27
5. $51,480.70
6. $410.64
7. $45,618.70
8. $1,756.44
9. $99.99
10. $2,071.84

Let me know if you'd like these rounded differently or need explanations in simpler terms!