On 5 April Lunga invested R75 000 in an account paying 8,37% interest per year, compounded monthly. Interest is credited on the 1st of every month. Lunga wants to open a second-hand cellphone shop in the new Talk-and-Listen complex. He will move into his new premises on 21 November of the same year.

If simple interest is used for odd period calculations and compound interest for the full term, then the amount of money that Lunga will have available in the account on 21 November is

To solve this problem, we need to calculate the total amount Lunga will have in his account on 21 November using both compound interest for the full months and simple interest for the odd period.

### Step 1: Calculate the compound interest for the full months
- **Principal (P)**: R75,000
- **Annual interest rate (r)**: 8.37% or 0.0837
- **Number of months (n)**: From 5 April to 1 November is 7 months.

The formula for compound interest is:

\[
A = P \left(1 + \frac{r}{12}\right)^n
\]

where:
- \( A \) is the amount after \( n \) months,
- \( P \) is the principal,
- \( r \) is the annual interest rate,
- \( n \) is the number of months.

Substitute the given values into the formula:

\[
A = 75,000 \left(1 + \frac{0.0837}{12}\right)^7
\]

\[
A = 75,000 \left(1 + 0.006975\right)^7
\]

\[
A = 75,000 \times (1.006975)^7
\]

Let's calculate this value.

### Step 2: Calculate the simple interest for the odd period
The odd period is from 1 November to 21 November, which is 20 days.

The formula for simple interest is:

\[
\text{Simple Interest} = P \times \frac{r}{100} \times \frac{t}{365}
\]

where:
- \( P \) is the amount calculated after 7 months of compound interest,
- \( r \) is the annual interest rate (8.37%),
- \( t \) is the time in days (20 days).

Finally, add the simple interest to the amount after 7 months to get the total amount on 21 November.

Let me calculate these values for you.Lunga will have approximately **R79,100.52** in his account on 21 November.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:

1. How would the final amount change if the interest was compounded daily instead of monthly?
2. What if Lunga wanted to withdraw money monthly—how would that affect his final amount?
3. How does the choice of compounding period (monthly, quarterly, etc.) impact the interest earned?
4. What would happen if the interest rate were slightly higher or lower, say 9% or 7.5%?
5. How would the calculation differ if the odd period was longer or shorter than 20 days?

**Tip:** Always ensure to convert time periods correctly when switching between compound and simple interest calculations.

Explore how Lunga's R75,000 investment grows with compound and simple interest calculations. Understand the impact of monthly compounding and simple interest over 20 days on his investment. Get a detailed solution for Lunga's financial planning.

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