Question

A bank offers a savings account that currently pays 2% interest per year compounded monthly. The amount of money in the account after t years, where t represents time in years, is represented by the expression P(1+0.02/12)^12t, where P represents the initial amount of money invested in the account and t represents the number of years the money has been invested. What will happen to the initial amount invested in the savings account when the interest rate changes from 2% to 2.25%?
A. The initial amount in the account does not change because it is a factor that is independent of both the interest rate and t.

B. The initial amount in the account does not change because it is a factor that is only dependent of t and not on the interest rate.

C. The initial amount in the account will change because it is a factor that is dependent on the interest rate but not on t.

D. The initial amount in the account will change because it is multiplied by a factor that is dependent on both the interest rate and t.

Answer 1

The appropriate choice is ...
.. A. The initial amount in the account does not change because it is a factor that is independent of both the interest rate and t.

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In general, each of the variables in a formula is independent of the others. (Occasionally, you'll see a formula where that is not true, but then the "variable" will likely be indicated as a function of those things it is dependent upon.)