On 16 April Bheka deposited an amount of money in a savings account that earns 8,5% simple interest. He intends to withdraw the balance of R2 599 on 8 December of the same year to buy his little sister a DVD player for Christmas. The amount of money that Bheka deposited is

a.
R2 465,46.

b.
R2 460,03.

c.
R2 461,82.

d.
R2 463,60.

To determine the amount of money Bheka deposited, we need to calculate the principal using the simple interest formula. The simple interest formula is:

\[ I = P \times r \times t \]

Where:
- \( I \) is the interest earned
- \( P \) is the principal amount (initial deposit)
- \( r \) is the annual interest rate (as a decimal)
- \( t \) is the time in years

We know the following:
- The interest rate \( r \) is 8.5% per year, which is 0.085 as a decimal.
- The final amount in the account is R2,599.
- The interest period is from 16 April to 8 December.

First, calculate the time \( t \) in years. 

From 16 April to 8 December is approximately:
- April: 15 days (assuming 16 April to 30 April)
- May: 31 days
- June: 30 days
- July: 31 days
- August: 31 days
- September: 30 days
- October: 31 days
- November: 30 days
- December: 8 days

Summing these days:
\[ 15 + 31 + 30 + 31 + 31 + 30 + 31 + 30 + 8 = 237 \text{ days} \]

Convert days to years:
\[ t = \frac{237}{365} \approx 0.6493 \text{ years} \]

Now, use the formula for the final amount with simple interest:
\[ A = P + I \]
\[ 2599 = P + P \times r \times t \]
\[ 2599 = P (1 + r \times t) \]

Substitute the values for \( r \) and \( t \):
\[ 2599 = P \left(1 + 0.085 \times 0.6493\right) \]
\[ 2599 = P (1 + 0.0551905) \]
\[ 2599 = P \times 1.0551905 \]

Solve for \( P \):
\[ P = \frac{2599}{1.0551905} \]
\[ P \approx 2463.60 \]

Therefore, the correct answer is:

d. R2 463,60

Would you like more details or have any questions?

Here are 8 related questions to expand your understanding:

1. How do you convert an annual interest rate to a decimal?
2. What is the difference between simple interest and compound interest?
3. How would the calculation change if the interest was compounded monthly?
4. Can you explain the concept of principal in simple interest?
5. What would be the effect of a higher interest rate on the principal required?
6. How do you calculate the number of days between two dates?
7. How does simple interest differ for shorter and longer time periods?
8. What is the formula for calculating the final amount in a simple interest scenario?

**Tip:** Always double-check your time period calculations, especially when dealing with dates and days, to ensure accuracy in financial computations.

Learn how to calculate the initial deposit Bheka made in his savings account using simple interest. This problem involves converting annual interest rates to decimals, calculating time periods, and applying the simple interest formula. Suitable for high school students studying financial mathematics.

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