Question

Marco says he will earn more interest on his $100 savings if he gets 4% interest compounded annually than if he gets 5% simple interest. How many years does he have to keep the money in the bank without withdrawig any to be right?

Answer 1

6 years

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 =
`(5)/(100)` *100 =$5

So the compound interest needs to be greater than $5 .

Lets calculate the compound interest over the years.

1st Year:
`(4)/(100)` *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

`(4)/(100)` *104 =$4.16

3rd Year: Again interest from 2nd year will be added

`(4)/(100)` *108.16 =$4.33

4th Year: Again interest from 3rd year will be added

`(4)/(100)` *112.49 =$4.49

5th Year:

`(4)/(100)` *116.99 =$4.68

6th Year:

`(4)/(100)` *121.67 =$4.87

7th Year:

`(4)/(100)` *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.