Solved 67 1 2 3 4 5 SIMPLE INTEREST WORKSHEET Question One | Chegg.com - Free Printable

Let's solve the Simple Interest Worksheet step by step using the formula:

$$
I = P \cdot r \cdot t
$$

Where:
- $ I $ = Interest
- $ P $ = Principal (initial amount)
- $ r $ = Annual interest rate (as a decimal)
- $ t $ = Time in years

Also, remember:
- $ A = P + I $ → Amount after interest
- Convert time appropriately: months → $ \frac{\text{months}}{12} $, days → $ \frac{\text{days}}{365} $, weeks → $ \frac{\text{weeks}}{52} $

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We'll go row by row and fill in missing values.

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Row 1

- $ P = 12,000 $
- $ r = 8\% = 0.08 $
- $ t = 3 $ years

$$
I = 12000 \times 0.08 \times 3 = 2880
$$
$$
A = 12000 + 2880 = 14880
$$

✔ Answer: $ I = 2880 $, $ A = 14880 $

---

Row 2

- $ P = 300,000 $
- $ r = 6.5\% = 0.065 $
- $ t = 9 $ months = $ \frac{9}{12} = 0.75 $ years

$$
I = 300000 \times 0.065 \times 0.75 = 14,625
$$
$$
A = 300000 + 14625 = 314,625
$$

✔ Answer: $ I = 14,625 $, $ A = 314,625 $

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Row 3

- $ P = 5500 $
- $ I = 162.74 $
- $ t = 180 $ days = $ \frac{180}{365} \approx 0.49315 $ years

Use $ I = P \cdot r \cdot t $ to find $ r $:

$$
r = \frac{I}{P \cdot t} = \frac{162.74}{5500 \times 0.49315} \approx \frac{162.74}{2712.325} \approx 0.0600
$$

So $ r \approx 6.00\% $

Now calculate $ A = P + I = 5500 + 162.74 = 5662.74 $

✔ Answer: $ r = 6.00\% $, $ A = 5662.74 $

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Row 4

- $ P = 1000 $
- $ I = 13.75 $
- $ t = 30 $ months = $ \frac{30}{12} = 2.5 $ years

Find $ r $:

$$
r = \frac{I}{P \cdot t} = \frac{13.75}{1000 \times 2.5} = \frac{13.75}{2500} = 0.0055 = 0.55\%
$$

$ A = 1000 + 13.75 = 1013.75 $

✔ Answer: $ r = 0.55\% $, $ A = 1013.75 $

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Row 5

- $ r = 1.5\% = 0.015 $
- $ t = 15 $ weeks = $ \frac{15}{52} \approx 0.28846 $ years
- $ I = 750.00 $

Find $ P $:

$$
P = \frac{I}{r \cdot t} = \frac{750}{0.015 \times 0.28846} = \frac{750}{0.0043269} \approx 173,333.33
$$

Check: $ 173333.33 \times 0.015 \times 0.28846 \approx 750 $

Then $ A = P + I = 173333.33 + 750 = 174,083.33 $

✔ Answer: $ P = 173,333.33 $, $ A = 174,083.33 $

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Row 6

- $ r = 3.5\% = 0.035 $
- $ t = 2 $ years
- $ I = 52.50 $

Find $ P $:

$$
P = \frac{I}{r \cdot t} = \frac{52.50}{0.035 \times 2} = \frac{52.50}{0.07} = 750
$$

$ A = 750 + 52.50 = 802.50 $

✔ Answer: $ P = 750 $, $ A = 802.50 $

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Row 7

- $ P = 1650 $
- $ r = 6.75\% = 0.0675 $
- $ I = 85.00 $

Find $ t $:

$$
t = \frac{I}{P \cdot r} = \frac{85}{1650 \times 0.0675} = \frac{85}{111.375} \approx 0.7632 \text{ years}
$$

Convert to months: $ 0.7632 \times 12 \approx 9.16 $ months ≈ 9 months and 5 days, but let’s keep it in years for now.

But we can leave $ t $ as $ \approx 0.7632 $ years.

Now $ A = 1650 + 85 = 1735 $

✔ Answer: $ t \approx 0.7632 $ years, $ A = 1735 $

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Row 8

- $ P = 1675 $
- $ r = 4.0\% = 0.04 $
- $ I = 315.25 $

Find $ t $:

$$
t = \frac{I}{P \cdot r} = \frac{315.25}{1675 \times 0.04} = \frac{315.25}{67} \approx 4.705 \text{ years}
$$

That's about 4 years and 8.46 months → approximately 4 years and 8.5 months

$ A = 1675 + 315.25 = 1990.25 $

✔ Answer: $ t \approx 4.705 $ years, $ A = 1990.25 $

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Row 9

- $ P = 4550 $
- $ r = 10\% = 0.10 $
- $ t = 91 $ days = $ \frac{91}{365} \approx 0.2493 $ years

$$
I = 4550 \times 0.10 \times 0.2493 \approx 4550 \times 0.02493 \approx 113.32
$$

$ A = 4550 + 113.32 = 4663.32 $

✔ Answer: $ I = 113.32 $, $ A = 4663.32 $

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Row 10

- $ P = 3200 $
- $ r = 7\% = 0.07 $
- $ t = 26 $ weeks = $ \frac{26}{52} = 0.5 $ years

$$
I = 3200 \times 0.07 \times 0.5 = 3200 \times 0.035 = 112
$$

$ A = 3200 + 112 = 3312 $

✔ Answer: $ I = 112 $, $ A = 3312 $

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Row 11

- $ r = 2.5\% = 0.025 $
- $ t = 6 $ months = $ 0.5 $ years
- $ I = 148.25 $

Find $ P $:

$$
P = \frac{I}{r \cdot t} = \frac{148.25}{0.025 \times 0.5} = \frac{148.25}{0.0125} = 11,860
$$

$ A = 11860 + 148.25 = 11,998.25 $

✔ Answer: $ P = 11,860 $, $ A = 11,998.25 $

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Row 12

- $ P = 3650 $
- $ t = 4 $ weeks = $ \frac{4}{52} \approx 0.07692 $ years
- $ I = 16.50 $

Find $ r $:

$$
r = \frac{I}{P \cdot t} = \frac{16.50}{3650 \times 0.07692} = \frac{16.50}{280.358} \approx 0.05886 \approx 5.89\%
$$

$ A = 3650 + 16.50 = 3666.50 $

✔ Answer: $ r \approx 5.89\% $, $ A = 3666.50 $

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## ✔ Final Completed Table:

| Principal (P) | Interest Rate (r %) | Time (t) | Interest (I) | Amount (A = P + I) |
|---------------|---------------------|----------------|----------------|---------------------|
| 12,000 | 8 | 3 years | 2,880 | 14,880 |
| 300,000 | 6.5 | 9 months | 14,625 | 314,625 |
| 5,500 | 6.00 | 180 days | 162.74 | 5,662.74 |
| 1,000 | 0.55 | 30 months | 13.75 | 1,013.75 |
| 173,333.33 | 1.5 | 15 weeks | 750.00 | 174,083.33 |
| 750 | 3.5 | 2 years | 52.50 | 802.50 |
| 1,650 | 6.75 | 0.7632 years | 85.00 | 1,735 |
| 1,675 | 4.0 | 4.705 years | 315.25 | 1,990.25 |
| 4,550 | 10 | 91 days | 113.32 | 4,663.32 |
| 3,200 | 7 | 26 weeks | 112 | 3,312 |
| 11,860 | 2.5 | 6 months | 148.25 | 11,998.25 |
| 3,650 | 5.89 | 4 weeks | 16.50 | 3,666.50 |

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Notes:

- All calculations use simple interest.
- Time conversions:
- 1 year = 12 months
- 1 year = 365 days
- 1 year = 52 weeks
- Answers are rounded to two decimal places where appropriate.

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