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.)

The situation described in this problem is a classic example of a **perpetuity** — a type of financial instrument that pays a fixed sum indefinitely. The formula for the present value $ PV $ of a perpetuity is:

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

where:
- $ PV $ is the present value (in this case, the amount deposited, $1,000),
- $ C $ is the annual payment (in this case, $75),
- $ r $ is the interest rate or rate of return (the unknown value we're solving for).

We can rearrange the formula to solve for the interest rate $ r $:

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

Substitute the values provided:

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

Thus, the interest rate $ r $ is:

\[
r = 0.075 = 7.5\%
\]

So, the interest rate the bank is advertising is **7.5%**.

Would you like more details on perpetuities or have any questions?

Here are 5 related questions:
1. How does a perpetuity differ from an annuity?
2. What is the formula for the present value of an annuity?
3. How do changes in the interest rate affect the value of a perpetuity?
4. What other financial instruments are similar to perpetuities?
5. How can perpetuities be used in real-life financial planning?

**Tip:** In finance, the perpetuity formula is a simple yet powerful tool to evaluate investments that promise indefinite payments.

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)?

Discover how to calculate the interest rate for a perpetuity with a $1,000 deposit and $75 annual payment. This example covers key finance concepts, including perpetuity and rate of return formulas, perfect for high school students in Grades 11-12.

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