Answer:
6 years
Step-by-step explanation:
Simple Interest: is the interest based on the principal amount.
Compound Interest: is the interest based on the principal amount and the interest that accumulates on it every year.
So 5% simple interest on $100 = [tex]\frac{5}{100}[/tex] *100 =$5
So the compound interest needs to be greater than $5 .
Lets calculate the compound interest over the years.
1st Year: [tex]\frac{4}{100}[/tex] *100 =$4
2nd Year: Now to calculate the interest in second year the interest in first year will be accumulated. So interest will be calculated on 100 +4 =$104
[tex]\frac{4}{100}[/tex] *104 =$4.16
3rd Year: Again interest from 2nd year will be added
[tex]\frac{4}{100}[/tex] *108.16 =$4.33
4th Year: Again interest from 3rd year will be added
[tex]\frac{4}{100}[/tex] *112.49 =$4.49
5th Year:
[tex]\frac{4}{100}[/tex] *116.99 =$4.68
6th Year:
[tex]\frac{4}{100}[/tex] *121.67 =$4.87
7th Year:
[tex]\frac{4}{100}[/tex] *126.54 =$5.06
In the 7th year, Marco will get compounded interest greater than $5, so he will have to keep money in the bank without withdrawing for 6 years.
