To find the present value (PV) using the formula for compound interest, we can use the following equation:

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

Where:

• $PV$ = Present value
• $FV$ = Future value ($679 in this case)
• $r$ = Annual interest rate (9.2% or 0.092)
• $n$ = Number of times the interest is compounded per year (monthly means $n = 12$)
• $t$ = Time in years (7 years)

Step-by-step solution:

1. Given values:

   • $FV = 679$
   • $r = 0.092$
   • $n = 12$
   • $t = 7$

2. Plug into the formula:

$PV = \frac{679}{(1 + \frac{0.092}{12})^{12 \times 7}}$

3. Simplify the denominator:

   • $\frac{0.092}{12} = 0.0076667$
   • $1 + 0.0076667 = 1.0076667$
   • $12 \times 7 = 84$
   • $(1.0076667)^{84} \approx 1.747422051$

4. Calculate the present value: $PV = \frac{679}{1.747422051} \approx 388.13$

Answer:

The present value is approximately $388.13.

Would you like more details on this solution, or do you have any other questions?

Related questions:

1. How does the number of compounding periods affect the present value?
2. How would the formula change if the interest were compounded annually instead of monthly?
3. What would the present value be if the interest rate were 5% instead of 9.2%?
4. If the goal is to achieve $1000 in 5 years at the same interest rate, what would the present value be?
5. How do you calculate compound interest when there is no set time period?

Tip:

The more frequently interest is compounded, the larger the present value needs to be to reach a specific future value.