Total capital 800000, interest 11.25 per annum, time 60 months, monthly withdrawal 17500.Balance after 60 months??

To calculate the remaining balance after 60 months with monthly withdrawals, we need to apply the concept of compound interest and account for the withdrawals. Here's how we can approach it step by step:

### Formula for Compound Interest with Withdrawals
The balance can be calculated using a formula that adjusts for regular withdrawals:
\[
A = P(1 + \frac{r}{n})^{nt} - W \left[ \frac{(1 + \frac{r}{n})^{nt} - 1}{\frac{r}{n}} \right]
\]
Where:
- \( A \) is the amount remaining after 60 months.
- \( P \) is the initial principal amount (800,000).
- \( r \) is the annual interest rate (11.25% or 0.1125).
- \( t \) is the time in years (60 months = 5 years).
- \( W \) is the monthly withdrawal amount (17,500).
- \( n \) is the number of times interest is compounded per year (assumed monthly, \( n = 12 \)).

Now let's calculate this step by step.

### Steps:
1. Initial capital \( P = 800,000 \)
2. Interest rate \( r = 0.1125 \)
3. Time \( t = 5 \) years
4. Monthly withdrawal \( W = 17,500 \)
5. Interest compounded monthly \( n = 12 \)

Let's calculate the balance after 60 months.After 60 months of withdrawing \(17,500\) per month and earning 11.25% annual interest, the account balance would be approximately \(-492.60\). This indicates that the withdrawals plus interest would deplete the initial capital, leaving a slight shortfall by the end of the 60 months.

Would you like further details or adjustments? Here are some related questions to explore:

1. What would the balance be with a lower withdrawal amount?
2. How would the balance change if the interest rate was higher?
3. What would the balance be if no withdrawals were made for the first year?
4. How would the result differ with quarterly compounding instead of monthly?
5. What happens if the withdrawal is increased by 5% annually?

**Tip:** Reducing withdrawals or increasing investment returns can help maintain a positive balance over time.

Total capital 800000, interest 11.25 per annum, time 60 months, monthly withdrawal 17500. Balance after 60 months??

Learn how to calculate the remaining balance after 60 months with a starting capital of 800,000, an annual interest rate of 11.25%, and monthly withdrawals of 17,500. Explore how compound interest and regular withdrawals affect the final amount. Suitable for students in Grades 11-12.

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