Suppose you invest $ 1 comma 050 in an account paying 5 % interest per year. a. What is the balance in the account after 2 years? How much of this balance corresponds to "interest on interest"? b. What is the balance in the account after 34 years? How much of this balance corresponds to "interest on interest"? a. What is the balance in the account after 2 years? The balance in the account (with compounded interest) after 2 years is $

Year 1 you would have:

$1,050 * (1+5%) = $1,102.5

Year 2:

$1,102.5 * (1+5%) = $1,157.6

"Interest on interest" is when you calculate the new interests considering the interest you earned in the past. In this case, you earned $52,50 in interest on year 1, and then you calculate interests on year 2 considering those $52,50 that you have earned before. On year 2 you earned $107.63 only in interests. If that wouldn't be "interest on interest" you should have earned the same $52,50 as on year 1. Then, the part of balance that corresponds to "interest on interest" is: $2.63. Because, without "interest on interest" you would have earned $52,50*2 = $105. but you earned $107.63, the difference between both is $2.63

Year 34, we use the compound interest formula:

Final Capital (FC) = Initial Capital (IC) * [ (1+interest (i)) ]^ (number of periods (n))

FC = 1,050 * (1+5%) ^34

FC = $5,516.02

Without "interest on interest" you should have earned $52,50*34=$1,785. Then at the end of year 34 you would have $1,050+1,785 = $2,835.