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.