To calculate how much you need to deposit today to have $11,250.00 in 6 years and 3 months (6.25 years), given a 7.92% annual interest rate compounded monthly, we use the formula for present value in compound interest:

$PV = \frac{FV}{(1 + i)^n}$

Where:

• $FV = 11,250.00$ (future value)
• $i = \frac{r}{m} = \frac{0.0792}{12}$ (monthly interest rate)
• $n = t \cdot m = 6.25 \cdot 12$ (total number of compounding periods)

Step 1: Compute monthly interest rate ($i$):

i = \frac{0.0792}{12} = 0.0066 \, \text{(or 0.66% per month)}

Step 2: Compute total number of compounding periods ($n$):

$n = 6.25 \cdot 12 = 75 \, \text{(months)}$

Step 3: Substitute values into the formula:

$PV = \frac{11,250.00}{(1 + 0.0066)^{75}}$

Step 4: Calculate:

$(1 + 0.0066)^{75} = 1.578031104$ $PV = \frac{11,250.00}{1.578031104} = 7,130.49$

Final Answer:

You need to deposit $7,130.49 today to have $11,250.00 in 6 years and 3 months at 7.92% interest compounded monthly.

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Do you have any questions or want more details?
Here are five related questions for practice:

1. How much would you have in the account after 10 years with the same conditions?
2. What if the interest rate was compounded quarterly instead of monthly?
3. What is the total interest earned over the 6 years and 3 months?
4. How does changing the compounding period affect the present value?
5. What would the present value be if the interest rate was 5% compounded monthly?

Tip: When solving compound interest problems, always double-check whether the interest is compounded annually, monthly, or at another frequency—it changes $n$ and $i$.