Luiza's savings account had $50 in its first year. Each year since then, her account accumulated interest amounting to 15% of the balance in the previous year.
Let g(n) be Luiza's account balance at the nth year of the saving.
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To find Luiza's account balance at the nth year, we can use the recursive equation:
g(n) = g(n-1) + 0.15 * g(n-1)
where g(n-1) represents the balance in the previous year.
To calculate her account balance at each year, we can start with the initial value of $50.
g(1) = $50
Then, for each subsequent year, we can calculate the account balance using the recursive equation.
g(2) = g(1) + 0.15 * g(1) = $50 + 0.15 * $50 = $50 + $7.5 = $57.5
g(3) = g(2) + 0.15 * g(2) = $57.5 + 0.15 * $57.5 = $57.5 + $8.625 = $66.125
g(4) = g(3) + 0.15 * g(3) = $66.125 + 0.15 * $66.125 = $66.125 + $9.91875 = $76.04375
Continuing this pattern, we can calculate Luiza's account balance for any given year by applying the recursive equation.