Final answer:
The amount that needs to be invested today at a 6.5% annual interest rate, compounded monthly, for the real value of the investment to be worth 100,000 EUR in ten years is approximately 63,194.32 EUR.
Step-by-step explanation:
To calculate the amount that needs to be invested today, we can use the formula for compound interest:
A = P(1 + r/n)ⁿ⁺
Where:
A = final amount
P = principal amount (the initial investment)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
Plugging in the given values:
A = 100,000
P = unknown
r = 6.5% = 0.065
n = 12 (compounded monthly)
t = 10
100,000 = P(1 + 0.065/12)¹²ˣ¹⁰
After solving this equation, we find that the principal amount (the amount that needs to be invested today) is approximately 63,194.32 EUR.