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Victoria had $200 in her account at the end of one year. At the first of each subsequent year she deposits $15 into the account and earns 2% interest on the new balance. Which recursive formula represents the total amount of money in the bank?

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W0lf93
Victoria initially has $200 in her account and she deposited $15 for the next year and earns an interest of 2%, then for the first year, her total balance is A(1) = 1.002(200 + 15) As for the year after that, A(2) = 1.002 [1.002(200 + 15) + 15] = 1.002^2(215) + 1.002(15) A(3) = 1.002{ [ 1.002^2(215) + 1.002(15)] } = 1.002^3(215) + 1.002^3(15) . . . A(t) = (1.002^t)(215) + [1.002^(t-1)](15) A(t) = [1.002^(t-1)][1.002(215) + 15] = 230.43 [ 1.002^(t-1) ] Therefore, the recursive formula that best represents the total amount of money in t years is A(t) = 230.43 [ 1.002^(t-1) ].

Answer:

A(t) = 200+15t(1+0.02)^{t}

Step-by-step explanation:

Since the interest is calculated on the new balance every year.

Hence the formula used for compound interest is:

A = P(1+[tex]\frac{r}{n}[/tex]^{nt}

where, A =Amount after t years

P =Principal amount

200 is the initial balance and Since, here the $15 is added to the balance each year. Therefore, P = 200+15t

r = rate each year (0.02)

t = time (in years) (t)

n = no. of times the interest is compounded in a year (n=1)

Therefore, the recursive formula is:

A(t) = 200+15t(1+0.02)^{t}

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