Final answer:
To have $10,000 in ten years with a 10% annual compounded interest rate, one would need to invest approximately $3,855.43 today.
Step-by-step explanation:
The question at hand involves calculating the present value of a future amount using compound interest. In the provided example, you need to determine how much money you should initially invest at a 10% annual compounded interest rate to have $10,000 in ten years. The formula for compound interest is P = A / (1 + r/n)^(nt), where:
- P is the present value (initial investment),
- A is the future value of the investment/loan, including interest,
- r is the annual interest rate (decimal),
- n is the number of times that interest is compounded per year, and
- t is the time the money is invested for, in years.
To find out how much you need to deposit now (P), you can plug in the values:
A = $10,000
r = 10% or 0.10
n = 1 (since it's compounded annually)
t = 10 years
Using the formula, you'd calculate the present value like this:
P = 10,000 / (1 + 0.10/1)^(1*10)
P = 10,000 / (1.10)^10
P = 10,000 / 2.59374
P ≈ $3,855.43
Therefore, the amount you need to invest today to have $10,000 in ten years with an interest rate of 10% compounded annually is approximately $3,855.43.