A local bank is running the following advertisement in the​ newspaper: "For just 

​$1 comma 0001,000 

we will pay you 

​$7575 

​forever!" The fine print says that for a 

​$1 comma 0001,000 

​deposit, the bank will pay 

​$7575 

every year in​ perpetuity, starting one year after the deposit is made. What interest rate is the bank advertising​ (what is the rate of return of this​ investment)?

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Part 1

The interest rate the bank is advertising is 

enter your response here​%. 

** ​(Round to two decimal​ places.)

This problem involves calculating the interest rate for a **perpetuity**, which is a type of annuity that pays out indefinitely.

The formula for the present value of a perpetuity is:

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

Where:
- $ PV $ is the present value (in this case, $1,000).
- $ C $ is the annual payment (in this case, $75).
- $ r $ is the interest rate (this is what we want to find).

To find the interest rate $ r $, we rearrange the formula:

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

Substitute the known values:

\[
r = \frac{75}{1000}
\]

Let's calculate this.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, the calculation for the interest rate can still be done manually. Using the formula:

\[
r = \frac{C}{PV} = \frac{75}{1000} = 0.075
\]

The interest rate $ r $ is 7.5%. 

If you have any questions or need further assistance, feel free to ask!

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A local bank is running the following advertisement in the newspaper: 'For just $1,000 we will pay you $75 forever!' The fine print says that for a $1,000 deposit, the bank will pay $75 every year in perpetuity, starting one year after the deposit is made. What interest rate is the bank advertising (what is the rate of return of this investment)?

Learn how to calculate the interest rate for a perpetuity based on a $1,000 deposit and $75 annual payment. This problem explains key financial concepts such as perpetuity and interest rate calculation, using the perpetuity formula. Ideal for high school students in Grades 10-12.

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