The account balance will be $7,152 three years from now.
Explanation:
The annual interest is 20%. The formula to calculate compound interest is
A = P × (1 + (r/n))^tn where A is the amount after adding the compound interest, P is the interest, r is the interest %, n is number of compounds per year and tn is the years to be calculated but since the interest is compounded yearly and we check the balance every year we get that the n and rn equal to 1 so we get that A = P (1 +r)^1
So for the beginning of the first year where principal is $1,500,
A = $1,500 (1 + 0.20) = $1,500 (1.20) = $1,800.
For the beginning of the second year, the current balance is $1,800 and another $1,650 is added so prinicipal P is equal to $1,800 + $1,650 = $3,450,
A = $3,450 (1 + 0.20) = $3,450 (1.20) = $4,140.
For the start of the third year, current balance is $4,140 and $1,820 is added so principal is $4,140 + $1,820 = $5,960,
A = $5,490 (1 + 0.20) = $5,490 (1.20) = $7,152.
