The statement, "After 12 years, Minerva's account balance should be about $100, assuming that she does not add or withdraw any money from the account", is true, given the graph of final balance after compounding annually.
What is compound interest?
Interest is the extra money you get as a reward for investing or saving your money with a bank or an institution.
The compound interest implies that the interest received in each period, is added to the sum, and the new interest is calculated on this cumulative sum.
The final amount of a compound interest account, for a sum of P, at a rate of interest r, after a time period n, is given as:
A = P(1 + r)ⁿ.
How to solve the question?
In the question, we are informed that Minerva starts a savings account with $50, where the interest on the account balance is compounded annually. The graph given, shows the account balance in terms of x, the number of years since the account was opened.
We are asked whether the statement, "After 12 years, Minerva's account balance should be about $100, assuming that she does not add or withdraw any money from the account", is true, false, or indeterminant.
From the graph given, the point when x, the number of years since the account was opened is 12 years, the corresponding balance f(x) = 100.
This implies, that after 12 years, Minerva's account balance should be about $100. So, the given statement is true.
Thus, the statement, "After 12 years, Minerva's account balance should be about $100, assuming that she does not add or withdraw any money from the account", is true, given the graph of final balance after compounding annually.
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