Compound Interest Worksheets - Math About - Free Printable

Sure! Let’s solve each of these compound interest problems step by step. The formula for compound interest is:

> A = P(1 + r/n)^(nt)

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

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Problem 1:

> You invested $52,400 at 6% compounded annually for 5 years. What is your total return on this investment?

Given:
- P = $52,400
- r = 6% = 0.06
- n = 1 (annually)
- t = 5

Formula:
A = 52400 × (1 + 0.06/1)^(1×5)
= 52400 × (1.06)^5
= 52400 × 1.3382255776
≈ $70,122.99

Total Return = A - P = 70,122.99 - 52,400 = $17,722.99

✔ Answer: $70,122.99 (or $17,722.99 return)

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Problem 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?

Given:
- P = $10,400
- r = 12.7% = 0.127
- n = 2 (semi-annually)
- t = 4

Formula:
A = 10400 × (1 + 0.127/2)^(2×4)
= 10400 × (1 + 0.0635)^8
= 10400 × (1.0635)^8
≈ 10400 × 1.635788
≈ $17,012.19

✔ Answer: $17,012.19

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Problem 3:

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

Given:
- P = $5,300
- r = 2.9% = 0.029
- n = 1
- t = 2

Formula:
A = 5300 × (1.029)^2
= 5300 × 1.058841
≈ $5,611.86

Return = 5611.86 - 5300 = $311.86

✔ Answer: $5,611.86 (or $311.86 return)

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Problem 4:

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

Given:
- P = $100
- r = 8.2% = 0.082
- n = 1
- t = 7

Formula:
A = 100 × (1.082)^7
≈ 100 × 1.73757
≈ $173.76

✔ Answer: $173.76

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Problem 5:

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

Given:
- P = $18,100
- r = 13.6% = 0.136
- n = 4 (quarterly)
- t = 7.5

Formula:
A = 18100 × (1 + 0.136/4)^(4×7.5)
= 18100 × (1 + 0.034)^30
= 18100 × (1.034)^30
≈ 18100 × 2.74533
≈ $49,690.47

✔ Answer: $49,690.47

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Problem 6:

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

Given:
- P = $270
- r = 15% = 0.15
- n = 1
- t = 3

Formula:
A = 270 × (1.15)^3
= 270 × 1.520875
≈ $410.64

✔ Answer: $410.64

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Problem 7:

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

Given:
- P = $43,000
- r = 3% = 0.03
- n = 1
- t = 2

Formula:
A = 43000 × (1.03)^2
= 43000 × 1.0609
≈ $45,618.70

Return = 45618.70 - 43000 = $2,618.70

✔ Answer: $45,618.70 (or $2,618.70 return)

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Problem 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?

Given:
- P = $1,200
- r = 5.1% = 0.051
- n = 2
- t = 7.5

Formula:
A = 1200 × (1 + 0.051/2)^(2×7.5)
= 1200 × (1 + 0.0255)^15
= 1200 × (1.0255)^15
≈ 1200 × 1.4618
≈ $1,754.16

✔ Answer: $1,754.16

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Problem 9:

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

Given:
- P = $95
- r = 5.2% = 0.052
- n = 2
- t = 1

Formula:
A = 95 × (1 + 0.052/2)^2
= 95 × (1.026)^2
= 95 × 1.052676
≈ $99.99

✔ Answer: $99.99

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Problem 10:

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

Given:
- P = $1,450
- r = 5.4% = 0.054
- n = 12 (monthly)
- t = 6 + 2/3 = 20/3 ≈ 6.6667 years

Formula:
A = 1450 × (1 + 0.054/12)^(12 × 20/3)
= 1450 × (1 + 0.0045)^(80)
= 1450 × (1.0045)^80
≈ 1450 × 1.43257
≈ $2,077.23

✔ Answer: $2,077.23

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## ✔ Final Answers Summary:

1. $70,122.99
2. $17,012.19
3. $5,611.86
4. $173.76
5. $49,690.47
6. $410.64
7. $45,618.70
8. $1,754.16
9. $99.99
10. $2,077.23

Let me know if you’d like to see any calculations broken down further or need help with graphing or comparing simple vs. compound interest!