To calculate how much the $75 would have grown to after 135 years at an interest rate of 2.45% compounded annually, we can use the formula for compound interest:

$A = P \left(1 + \frac{r}{n}\right)^{nt}$

Where:

• $A$ is the final amount
• $P$ is the initial principal (the $75)
• $r$ is the annual interest rate (2.45% or 0.0245)
• $n$ is the number of times the interest is compounded per year (for annual compounding, $n = 1$)
• $t$ is the number of years (135 years)

Substituting the given values into the formula:

$A = 75 \left(1 + \frac{0.0245}{1}\right)^{1 \times 135}$

Now, I'll calculate the amount $A$.If your great-great-grandmother had deposited the $75 in a savings account earning 2.45% compounded annually, after 135 years, the amount in the account would now be approximately $1,968.69.

Would you like more details, or do you have any questions?

Here are five related questions:

1. How would the total amount change if the interest were compounded monthly instead of annually?
2. What would happen if the interest rate were slightly higher or lower?
3. How much would be accumulated in half the time (67.5 years)?
4. How does inflation affect the value of $1,968.69 over 135 years?
5. What if she had deposited $75 every year for 135 years?

Tip: When interest is compounded more frequently, the total accumulation grows faster due to more frequent application of interest on interest.