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This problem asks for the initial amount of money to deposit in a bank to ensure a monthly donation of $1076 in perpetuity, with a monthly interest rate of 1.5%.

To find the required initial deposit, we use the formula for a perpetuity:

\[
P = \frac{C}{r}
\]

where:
- $ P $ is the principal (initial deposit),
- $ C $ is the monthly payment amount,
- $ r $ is the monthly interest rate.

### Given values:
- $ C = 1076 $ dollars (monthly donation),
- $ r = 1.5\% = 0.015 $ (monthly interest rate).

### Solution:
Plugging in the values:

\[
P = \frac{1076}{0.015}
\]

Calculating this:

\[
P = \frac{1076}{0.015} = 71733.33
\]

Rounding to the nearest integer, we get:

\[
P \approx 71733 \text{ dollars}
\]

### Answer:
The initial deposit required is **$71,733**.

Would you like more details or have any questions? Here are some related questions to explore:

1. What if the monthly donation amount changes to $1200?
2. How does the required principal change with different interest rates?
3. What is the impact of compounding the interest monthly instead of using simple interest?
4. How much will the bank have in total after 10 years, assuming no withdrawals?
5. How would the calculation differ if the payment frequency changed from monthly to annually?

**Tip:** For perpetuity calculations, the interest rate must match the payment frequency (e.g., monthly rates for monthly payments).

En su testamento un filántropo solicitó que se entregará a un banco la cantidad de dinero necesaria para que se le donará al ancianato local 1076 dólares mensualmente a perpetuidad. La primera mensualidad se entregará a un mes del fallecimiento del filántropo. Sin embargo, el mismo día del fallecimiento se realizó un depósito al banco que administra la donación. El interés mensual ofrecido por el banco es de 1.5%. El dinero de la herencia que se debe destinar para cumplir la solicitud del filántropo es _____ dólares.

Determine the initial deposit required to ensure a perpetual monthly donation of $1076 with a bank interest rate of 1.5% per month. Explore key concepts in perpetuity and algebra, perfect for students in Grades 10-12.

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