Option 3: Simple interest versus Compound interest
Grant is after a short term investment of 5 years with an initial investment of $5000.
Grant went to two different banks and was offered the following:
Bank A:  Simple interest of
12.9% p.a.
Bank B: Compound interest of 10.4675% p.a.
What is the best option for Grant? What is the difference in the interest earned between the two options?

To determine which investment option is best for Grant, we will calculate the interest earned from both Bank A (with simple interest) and Bank B (with compound interest) over the 5-year period. Then, we will compare the results.

### 1. Bank A: Simple Interest
Simple interest is calculated using the formula:
\[
I = P \times r \times t
\]
Where:
- $ I $ is the interest earned,
- $ P $ is the principal (initial investment),
- $ r $ is the annual interest rate (as a decimal),
- $ t $ is the time (in years).

Given:
- $ P = 5000 $,
- $ r = 12.9\% = 0.129 $,
- $ t = 5 $ years.

The interest earned with Bank A will be:
\[
I = 5000 \times 0.129 \times 5
\]

### 2. Bank B: Compound Interest
Compound interest is calculated using the formula:
\[
A = P \times \left(1 + \frac{r}{n}\right)^{n \times t}
\]
Where:
- $ A $ is the final amount (principal + interest),
- $ P $ is the principal,
- $ r $ is the annual interest rate (as a decimal),
- $ n $ is the number of times interest is compounded per year,
- $ t $ is the time (in years).

Given:
- $ P = 5000 $,
- $ r = 10.4675\% = 0.104675 $,
- $ t = 5 $ years,
- $ n = 1 $ (since the compounding period is not specified, we'll assume annual compounding).

The total amount in Bank B after 5 years will be:
\[
A = 5000 \times \left(1 + 0.104675\right)^5
\]

Let me calculate the interest earned and the difference between the two options.# Given values for the problem
P = 5000  # Principal amount in dollars
t = 5  # Time in years

# Bank A: Simple interest calculation
r_simple = 0.129  # Simple interest rate (12.9% per annum)

# Calculate simple interest
I_simple = P * r_simple * t

# Bank B: Compound interest calculation
r_compound = 0.104675  # Compound interest rate (10.4675% per annum)
n = 1  # Compounding once per year

# Calculate compound interest (final amount after 5 years)
A_compound = P * (1 + r_compound / n)**(n * t)

# Interest earned in Bank B is the final amount minus the initial principal
I_compound = A_compound - P

# Calculate the difference in interest earned between Bank A and Bank B
difference = I_compound - I_simple

I_simple, I_compound, differenceThe interest earned over 5 years is as follows:

- **Bank A (Simple Interest)**: $3,225.00
- **Bank B (Compound Interest)**: $3,225.13

The difference in the interest earned between the two options is approximately **$0.13**, with Bank B yielding slightly more interest due to compounding.

Given this small difference, both options are nearly identical, but technically **Bank B** (compound interest) offers a slight advantage.

Do you want more details or have any questions?

Here are 5 related questions you might find interesting:
1. How does the frequency of compounding affect the interest earned?
2. What would happen if Grant invested for more than 5 years?
3. How would monthly compounding change the outcome for Bank B?
4. What if the initial investment amount was different?
5. How do simple interest and compound interest compare for longer-term investments?

**Tip:** The impact of compound interest grows significantly with time and more frequent compounding.

Compare simple interest and compound interest for a short-term investment of $5000 over 5 years. Understand how each bank's interest rates affect the total interest earned. Bank A offers 12.9% p.a. simple interest, while Bank B offers 10.4675% p.a. compound interest. Find out which option yields more interest and why. Ideal for high school students studying finance and interest calculations.

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