Compare simple and compound interest worksheet featuring six problems on investment returns.

Here are the step-by-step solutions for each problem on the worksheet.

To solve these, we compare two formulas:
1. Simple Interest (Option A): The money grows by the same amount every year based on the original starting amount.
* Formula: $Total = P \times (1 + r \times t)$
2. Continuous Compound Interest (Option B): The money grows faster over time because interest is added constantly to the growing balance.
* Formula: $Total = P \times e^{(r \times t)}$

*Note: In all comparison questions (1–5), we assume the starting investment ($P$) is the same for both options, so we can just compare the growth multipliers.*

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Problem 1

Scenario: Option A is 9.8% simple interest. Option B is 8.3% compounded continuously. Time is 15 years.

Step 1: Calculate Option A multiplier
Formula: $1 + (rate \times time)$
$1 + (0.098 \times 15) = 1 + 1.47 = 2.47$
(This means your money becomes 2.47 times the original amount).

Step 2: Calculate Option B multiplier
Formula: $e^{(rate \times time)}$
Exponent: $0.083 \times 15 = 1.245$
Calculation: $e^{1.245} \approx 3.47$
(This means your money becomes roughly 3.47 times the original amount).

Comparison:
$3.47 > 2.47$. Option B results in much more money.

Final Answer: Option B

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Problem 2

Scenario: Option A is 9.5% simple interest. Option B is 7.2% compounded continuously. Time is 14 years.

Step 1: Calculate Option A multiplier
$1 + (0.095 \times 14) = 1 + 1.33 = 2.33$

Step 2: Calculate Option B multiplier
Exponent: $0.072 \times 14 = 1.008$
Calculation: $e^{1.008} \approx 2.74$

Comparison:
$2.74 > 2.33$. Option B is better.

Final Answer: Option B

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Problem 3

Scenario: Option A is 9.9% simple interest. Option B is 7.5% compounded continuously. Time is 11 years.

Step 1: Calculate Option A multiplier
$1 + (0.099 \times 11) = 1 + 1.089 = 2.089$

Step 2: Calculate Option B multiplier
Exponent: $0.075 \times 11 = 0.825$
Calculation: $e^{0.825} \approx 2.28$

Comparison:
$2.28 > 2.089$. Option B is better.

Final Answer: Option B

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Problem 4

Scenario: Option A is 7.2% simple interest. Option B is 5.5% compounded continuously. Time is 15 years.

Step 1: Calculate Option A multiplier
$1 + (0.072 \times 15) = 1 + 1.08 = 2.08$

Step 2: Calculate Option B multiplier
Exponent: $0.055 \times 15 = 0.825$
Calculation: $e^{0.825} \approx 2.28$

Comparison:
$2.28 > 2.08$. Option B is better.

Final Answer: Option B

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Problem 5

Scenario: Option A is 9.4% simple interest. Option B is 7% compounded continuously. Time is 12 years.

Step 1: Calculate Option A multiplier
$1 + (0.094 \times 12) = 1 + 1.128 = 2.128$

Step 2: Calculate Option B multiplier
Exponent: $0.07 \times 12 = 0.84$
Calculation: $e^{0.84} \approx 2.32$

Comparison:
$2.32 > 2.128$. Option B is better.

Final Answer: Option B

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Problem 6

Scenario: Lynn invests $560.
Option A: 7.5% simple interest.
Option B: 6.1% compounded continuously.
Time: 9 years.
Question: How much *more* does she have in Option B than Option A?

Step 1: Calculate Total for Option A (Simple)
Formula: $A = P(1 + rt)$
$A = 560 \times (1 + (0.075 \times 9))$
$A = 560 \times (1 + 0.675)$
$A = 560 \times 1.675$
$A = \$938.00$

Step 2: Calculate Total for Option B (Continuous)
Formula: $A = Pe^{rt}$
Exponent: $0.061 \times 9 = 0.549$
$A = 560 \times e^{0.549}$
$A = 560 \times 1.7315...$
$A \approx \$969.66$ (rounded to two decimal places)

Step 3: Find the Difference
Difference = Option B Total - Option A Total
Difference = $969.66 - 938.00$
Difference = $31.66$

Final Answer: $31.66