Final answer:
The equation to determine the annual deposit needed to reach $3,000,000 in 10 years with a 10% interest rate is P = $3,000,000 x {0.10/[(1 + 0.10)^10 - 1]}.
Step-by-step explanation:
To determine how much the company needs to deposit each year to reach $3,000,000 in 10 years with an interest rate of 10%, we can use the formula for the future value of an annuity, which is given by:
FV = P \times \frac{[(1 + r)^n - 1]}{r}
Where:
- FV is the future value of the annuity (the amount you want to have in the future).
- P is the annual payment (the amount you deposit each year).
- r is the interest rate per period.
- n is the number of periods.
Rearranging the formula to solve for P (annual payment) gives us:
P = FV \times \frac{r}{[(1 + r)^n - 1]}
Substituting the given values (FV = $3,000,000, r = 0.10, n = 10) into the formula, we can calculate the annual payment that needs to be made.
Therefore, the equation representing the annual deposit required is:
P = $3,000,000 \times \frac{0.10}{[(1 + 0.10)^10 - 1]}