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, compounded annually. Which recursive formula represents the total amount of money in Victoria’s account at the end of the nth year?

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+r/n^{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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step-by-step explanation: