Final answer:
To calculate the number of years it will take for Arthur to get the cost of the speedboat, we can use the formula for compound interest. Based on the given options, it would take 5 years for Arthur's investment to reach the cost of the speedboat. Option D is the Correct Answer.
Step-by-step explanation:
To calculate the number of years it will take for Arthur to get the cost of the speedboat, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the amount of money accumulated after t years
- P is the principal amount (initial investment)
- r is the annual interest rate (in decimal form)
- n is the number of times the interest is compounded per year
- t is the number of years
In this case, Arthur invested 18,483 EUR at a nominal annual interest rate of 3.6%, compounded monthly (n = 12). Let's calculate the number of years it will take for the investment to reach the cost of the speedboat:
A = 18,483(1 + 0.036/12)^(12t)
Using the information given in the options, we can check how many years it would take to reach the cost of the speedboat:
- Option A) 2 years: A = 18,483(1 + 0.036/12)^(12*2) = $19,675.21
- Option B) 3 years: A = 18,483(1 + 0.036/12)^(12*3) = $20,909.92
- Option C) 4 years: A = 18,483(1 + 0.036/12)^(12*4) = $22,198.78
- Option D) 5 years: A = 18,483(1 + 0.036/12)^(12*5) = $23,546.34
Based on these calculations, it would take 5 years (Option D) for Arthur's investment to reach the cost of the speedboat.