Final answer:
The initial deposit needed to have $10,000 in 10 years at a 10% annual compound interest rate is approximately $3,855.43. There isn't an exact match among the answer choices, but the closest one would be Option C, assuming there's a discrepancy in the options provided.
Step-by-step explanation:
To determine the initial deposit needed to accumulate $10,000 in 10 years with an annual compound interest rate of 10%, we use the formula for compound interest:
P = A / (1 + r)^nWhere:
P is the principal (initial deposit),
A is the amount of money accumulated after n years, including interest,
r is the annual interest rate (decimal),
n is the number of years the money is invested.
Given:
A = $10,000, r = 10% or 0.10, n = 10 year
Substituting these values into the formula:
P = $10,000 / (1 + 0.10)^10
P = $10,000 / (1.10)^10
P = $10,000 / 2.59374
P = $3,855.43 approximately
Therefore, the initial deposit that needs to be made is not exactly one of the provided options; however, the closest answer to this computed value would be Option C) $1,041.20, assuming there was a typo or another reason for the discrepancy in the provided options.