Final answer:
To find the sum of money that will amount to €8,900 after 5 years with a compound interest rate of 6% per annum, we can use the formula for compound interest: A = P(1 + r/n)^(nt). Plugging in the given values and solving the equation, the initial sum of money that needs to be invested is approximately €7,500.
Step-by-step explanation:
To find the sum of money that will amount to €8,900 after 5 years with a compound interest rate of 6% per annum, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times interest is compounded in a year, and t is the number of years.
Plugging in the given values, we get:
A = P(1 + 0.06/1)^(1*5)
Simplifying the equation, we have:
8900 = P(1.06)^5
Dividing both sides by (1.06)^5, we find:
P = 8900 / (1.06)^5 ≈ €7500
Therefore, the initial sum of money that needs to be invested is approximately €7500. So the correct answer is (b) €7,500.