Student in a finance class surveyed 20 percent of the account holders at Docven Bank to determine whether the bank's "Stock Market Special" savings account actually paid account holders the promised 10 percent annual interest rate. The scatterplot above shows the data the students collected from account holders about how long ago they opened their accounts and their current balances. The students calculated a lone of best fit with the equation `y = 120(1+(.08)/(12))^(12x),` whihc means that the bank was actually paying account holders only an 8 percent annual interest rate. Which of the following best explains how the number 120 in the equation relates to the scatterplot?

Options

A. A "Stock Market Special" account with `$120` initially will likely have less than `$350` after 15 years.
B. All "Stock Market Special" accounts started with a `$120` initial investment.
C. The difference between the promised 10 percent annual interest rate and the actual 8 percent rate is `$120` a year.
D. A "Stock Market Special" account with `$120` initially will likely have more than `$350` after 15 years.

Answer

D

Explanation

In the line of best fit equation that the students calculated, the initial principal is `$120,` but that does not necessarily mean that all of the account holders had that much in the account initially. Eliminate (B).
To test (A) and (D), sketch in the line of best fit:

Notice that the line of best fit, which is based on an initial principal of `$120,` is definitely above `$350` at the 15 year mark, so (D) is correct. Since the line of best fit is exponential, not linear, there will not be a consistent difference between the 10 percent annual rate and 8 percent annual rate, which makes (C ) incorrect.