Answer :
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)
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.
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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}
